Study Guide for ECO 3411

Study Guide for Business Statistics and Applications--Soskin and Braun

Study Guide for Business Statistics and Applications

ECO 3411 Quantitative Business Tools II

Copyright 2012 University of Central Florida

College of Business Administration

Authors: Drs. Mark Soskin and Bradley Braun

Associate Professors of Economics

Not for resale or any other commercial use.

ALL INTELLECTUAL MATERIALS IN THIS TEXT ARE THE SOLE PROPERTY OF THE AUTHORS.

Business Statistics and Applications--Soskin and Braun

A. REVIEW QUESTIONS FOR CHAPTER 1 .................................................................... 2

Answers for Chapter 1 .............................................................................................................................................................. 2

B. REVIEW QUESTIONS FOR CHAPTER 2 .................................................................... 3

Answers for Chapter 2 .............................................................................................................................................................. 4

C. REVIEW QUESTIONS FOR CHAPTER 3 .................................................................... 5

Answers for Chapter 3 ............................................................................................................................................................ 16

D. REVIEW QUESTIONS FOR CHAPTER 4 ...................................................................17


E. REVIEW QUESTIONS FOR CHAPTER 5 ...................................................................38


F. REVIEW QUESTIONS FOR CHAPTER 6 ...................................................................40


G. REVIEW QUESTIONS FOR CHAPTER 7 ...................................................................52


H. REVIEW QUESTIONS FOR CHAPTER 8 ...................................................................58

Answers for Chapter 8: ........................................................................................................................................................... 64

I. REVIEW QUESTIONS FOR CHAPTER 9 ...................................................................65

Answers for Chapter 9: ........................................................................................................................................................... 68

J. REVIEW QUESTIONS FOR CHAPTER 10 .................................................................69

Answers for Chapter 10 .......................................................................................................................................................... 80

K. REVIEW QUESTIONS FOR CHAPTER 11 .................................................................81

Answers for Chapter 11 ........................................................................................................................................................ 104

L. REVIEW QUESTIONS FOR CHAPTER 12 ...............................................................105

Answers for Chapter 12 ........................................................................................................................................................ 108

Business Statistics and Applications--Soskin and Braun Page 2

A. Review Questions for Chapter 1 1.1 _______ is defined as the total collection of items under consideration. a. Population b. Variable c. Data d. Statistics 1.2 Statistics is an important tool because:

a. Statistics helps us to tell the datas story. b. People rarely deal with raw data. c. It can be used to unlock new sources of economic value. d. All the above are true.

1.3 The key steps for statistical decision making include identifying the population

and variables, locating the data, analyzing the data, and generating a report. Usually the most difficult step is

a. Identifying the relevant population and variables. b. Locating the data c. Analyzing the data. d. Generating a report.

1.4 Which is an ethical violation by a statistician or manager? a. Withholding information or distorting results to support a preferred conclusion b. Selling personal information to the highest bidder c. Having strong security to prevent hackers from stealing data d. Making profits from other peoples personal information e. all the above

Answers for Chapter 1

1.1: a, 1.2: d, 1.3: b, 1.4: a.


B. Review Questions for Chapter 2 2.12 Which of the following method of displaying the data would be best for a

data set with 450 observations?

a. a sorted listing

b. a listing of descriptive summary statistics

c. a histogram

d. all of the above are equally informative

e. it depends on the analytical problem at hand

2.13 A histogram presents quantitative data as

a. a table of frequencies

b. a pie chart of relative frequencies

c. bar graph of class frequencies

d. a sorted listing

e. a listing of descriptive statistics

2.14 The modal class is

a. the class with the largest observations

b. the class with the most observations

c. the class with the widest interval width

d. the most frequently occurring observation

e. the class containing the mode

2.44 Bivariate data are data gathered on

a. one variable for each observation

b. two variables for each observation

c. at least one variable for each observation

d. at least two variables for each observation

e. none of the above


2.45 A scatterplot is a

a. two dimensional plot of data

b. frequency distribution

c. histogram

d. trend line

e. random array of points

2.46 An index

a. summarizes a group of related variables

b. is the average of several variables

c. is often used to represent overall movements in stock prices

d. is often used to represent overall movements in consumer prices

e. all of the above

2.48 Which of the following is a guideline for constructing time series graphs?

a. place time on the vertical axis

b. always draw a trend line rather than connect the plotted points

c. beware of graphs that omit the most recently available data

d. compare each time series observation with its cross section counterpart

e. graph two (or more) time series variables on the same graph to compare

them

Answers for Chapter 2 2.12: c, 2.13: c, 2.14: b, 2.44: b, 2.45: a, 2.46: e, 2.48: c.


C. Review Questions for Chapter 3 3.1 The center of the distribution for salaries (measured in thousands of dollars /

year) 10, 20, 20, 20, 30, 100, 500 is a. 100 b. 20 c. the mean. d. the median. e. both b and d. 3.2 For 120 private colleges, the mean number of accounting majors is 84, the

median is 59, the mode is 64. In the histogram of accounting majors at the 120 colleges, the modal class

a. has a class midpoint of 59 accounting majors b. has a class midpoint of 64 accounting majors c. has a class midpoint of 84 accounting majors d. will not occur because this is not quantitative data e. cannot be found from information given in the problem 3.3 A housing tract builder needs to decide on the number of bedrooms to put

into its most commonly-built homes. Which measure of the average should the builder determine?

a. the mean number of bedrooms for new home sales b. the median number of bedrooms for new home sales c. the mode for bedrooms of new home sales d. the mean family size of new home buyers e. none of the above 3.4 In calculating the standard deviation which operation is not involved? a. summation over the number of observations b. squaring differences from the mean c. averaging over the number of observations d. taking the square root e. all the above operations are involved


3.5 The median is a. the arithmetic average b. the most frequently occurring value in the data set c. the 50th percentile d. the middle value if there is an even number of observations e. all of the above 3.6 For which of the following are the mean, median, and mode identical? a. 1 3 3 b. 1 2 2 4 c. 1 1 4 4 4 8 8 d. 1 10 10 19 e. 1 5 5 5 10 3.7 The median for the salaries (measured in thousands of dollars / year) 10, 20,

20, 20, 30, 100, 500 is a. 10 b. 20 c. 30 d. 65 e. 100 3.8 The mode for the salaries (measured in thousands of dollars / year) 10, 20,

20, 20, 30, 100, 500 is a. 10 b. 20 c. 30 d. 65 e. 100


3.9 If mean and median salaries are very similar at a firm, then you should conclude that

a. most employees make about the same salary b. if some salaries are far below the mean, other salaries are considerably

above the mean c. no salaries are far from the mean d. some salaries may be far above the mean, but none can be far below it e. the similarity between mean and median tells us nothing about the

distribution of the data 3.10 Given the following means, for which would you also want to know the

dispersion? a. choosing among three mutual funds which averaged 15, 12, and 8 percent

return b. hiring a new engineer from among graduates with 3.3, 3.1, and 3.0 grade

point averages c. attempting to make vacation reservations at one of three resort areas with

average annual occupancy rates of 60, 70, and 80 percent d. all of the above e. none of the above 3.11 If the mean weight of 50 parts in a shipment is 2.2 pounds and the median

weight is 0.8 pounds, the total weight of the shipment is a. 40 pounds b. 50 pounds c. 110 pounds d. 220 pounds e. cannot be determined from the information provided 3.12 If the mean weight of 50 parts in a shipment is 2.2 pounds and the median

weight is 0.8 pounds, then a. half the parts weigh more than 0.8 pounds b. 26 parts weigh less than 0.8 pounds c. 25 parts weigh between 0.8 and 2.2 pounds d. all of the above e. none of the above


3.13 For the data set 5 4 3 2 1 0 a. the mean and median are the same b. the mean has a value that does not occur in the data c. the median has a value that does not occur in the data d. all of the above e. none of the above 3.65 Which of the following is not a measure of dispersion? a. standard deviation b. range c. maximum d. mean absolute difference e. all of the above are measures of dispersion 3.66 The problem with using the range to determine dispersion is that the range

does not take account of a. the smallest value b. the largest value c. the difference between the largest and smallest value d. values other than the largest and smallest e. none of the above 3.67 In calculating the standard deviation which operation is not involved? a. summation over the number of observations b. squaring differences from the mean c. averaging over the number of observations d. obtaining the square root e. all the above operations are involved 3.80 Random samples a. must be collected from lottery machines b. are the results of simulations c. have the same chance of occurring as any other sample of the same size d. require a computer to collect e. none of the above


3.81 Which of the following is an example of random sampling? a. people attending a shopping mall on a weekday afternoon b. respondents to an evening phone survey c. a mailed questionnaire sent to people with drivers licenses d. phone response to a 900 number announced during the network evening

news e. drawing 10 names from a well-mixed hat containing names of everyone in

the population 3.82 A description of a variable in the population is a(n) a. estimator b. estimate c. parameter d. sample e. none of the above 3.83 Statistical inference is the process of a. describing a population from population data b. describing a sample using sample data c. make guesses about sample estimates by using population parameters d. make guesses about population parameters by using sample estimates e. all of the above 3.84 is the parameter but is an estimator of the mean __ a. X and __ b. X and M __ c. m and X __ d. and X e. none of the above


3.85 If the mean for a very large number of samples is equal to the parameter being estimated, the estimator is

a. unbiased b. a sample c. not an outlier d. random e. none of the above 3.86 An outlier is defined as a. an observation considerably larger than any other in the sample b. an observation considerably smaller than any other in the sample c. an observation considerably larger or smaller than any other in the sample d. observations that are measured incorrectly e. observations that should be deleted from the sample 3.87 Which of the following conclusions does not involve potentially large

sampling bias? a. poverty cannot be difficult to overcome. All the people I know that came

from the ghetto are doing well financially now. b. I can't see why our product isn't selling. Our most trusted customers tell

me we have the best product on the market. c. I knew I wanted to become a computer programmer. I loved computers

playing around with the one at home for years. d. I took art courses in school, so I know that I am not artistically inclined. e. All of the above involve sampling bias. 3.88 To ensure that s has the same units and scale as the variable in the data, a. we divide by n - 1 b. we square the differences from the mean c. we sum all the squared differences d. we take the square root of the final mean sum of squares e. none of the above


3.89 To adjust for the lost degree of freedom in the sample estimator s a. we divide by n - 1 b. we square the differences from the mean c. we sum all the squared differences d. we take the square root of the final mean sum of squares e. none of the above 3.90 For a utility company responding to the 200 service outages last month,

median repair time was 45 minutes, the mean was one and one-half hours, the minimum was 15 minutes, the maximum was 1 day, and the standard deviation was 3 hours. The range of service outage times last month was

a. 23.85 hours b. 23.75 hours c. 23.55 hours d. 23.25 hours e. 22.50 hours 3.91. The list price of new mid- and full-sized cars models was surveyed and the

summary statistics reported below: Variable N Mean Median TrMean StDev SEMean PRICE 45 22795 20389 22620 6486 967 Variable Min Max Q1 Q3 PRICE 13206 35553 17091 27357 Answer the following four questions regarding the data described above: 1. The median price, $20,389, must be an actual car price in the data set

because: a. there is an odd number of car models in the data set b. the average of the minimum and maximum is the median c. the median and mode always are actual observed values, but the mean

may not be d. the median is less than the mean e. the median does not have to be an actual car price in this data set


2. $22,347 is a. The interquartile range b. The range c. The standard deviation d. The mode e. None of the above 3. If the distribution of prices is approximately bell-shaped, then we would

expect about 95% of the prices would lie between: a. $16,309 and $29,281 b. $12,972 and $33,361 c. $9823 and $35,767 d. $17,091 and $27,357 e. None of the above 4. If a car dealer were to stock one of each of the 45 cars models, the total

value of its inventory would be approximately: a. $600,000 b. $750,000 c. $900,000 d. $1 million e. Cannot be calculated from the information given

3.92. In the 1993 NBA college draft, the 54 players drafted signed for annual

salaries (in thousands of dollars) given in the following sorted data listing, summary statistics, and histogram:

SALARY 125 125 125 125 125 145 160 170 175 200 220 245 275 300 305 325 365 380 400 430 475 500 550 575 600 625 660 700 745 775 800 825 865 900 950 1000 1100 1250 1300 1430 1500 1600 1700 1780 1875 1945 2000 2100 2200 2260 2335 2350 2400 2500 Variable N Mean Median TrMean StDev SEMean SALARY 54 924 680 881 752 102 Variable Min Max Q1 Q3 SALARY 125 2500 294 1525


Answer the following six questions based on this information: 1. The median annual salary is a. the average of the 27th and 28th highest salary b. half-way between $660,000 and $700,000 c. not an actual observation in the data set d. all of the above are true e. none of the above are true 2. The mode for this data set is a. $125,000 b. $250,000 c. $680,000 d. $924,000 e. none of the above 3. The modal class interval is a. $100,000 to $400,000 b. $125,000 to $2,500,000 c. $294,000 to $1,525,000 d. $924,000 to $2,628,000 e. none of the above 4. If a players union representative stated that one-third of the first-year

players drafted earned less than $400,000 per year, he would be reporting information about the

a. mean b. median c. mode d. modal class e. minimum

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5. The fiftieth percentile for annual salary of NBA rookies was a. more than a million dollars b. just over $900,000 dollars c. about half-a-million dollars d. under $700,000 e. cannot be determined from the information given 6. By only examining the histogram for the salary data, we can immediately

conclude that a. The mean will be substantially larger than the median b. There are outliers in the data c. Salaries do not have a bell-shaped distribution d. The standard deviation will be relatively large e. All of the above

3.93. A regional supervisor for Coors has the price per 6-pack of its beer surveyed

from the 25 supermarket chains in Los Angeles. Describe in a couple sentences the average and variability of beer prices from the following computer output of descriptive statistics:

N MEAN MEDIAN TRMEAN STDEV SEMEAN coors 25 3.6620 3.6500 3.6548 0.2446 0.0487 MIN MAX Q1 Q3 coors 3.2900 4.2900 3.4900 3.8200


3.94 New television shows are notoriously risky ventures. Nielsen ratings are the main variable used to assess the success of a show and the rates that can be charged advertisers. A network programmer would like you to summarize the Nielsen ratings for the 1993-94 season crop of new shows. You obtain the following computer printout:

Data Display NIELSEN 4.8 5.0 5.3 5.5 5.8 6.1 7.0 7.2 7.4 7.6 7.6 7.8 7.9 8.0 8.3 8.3 8.5 9.0 9.1 9.1 9.2 9.4 9.5 10.2 10.3 10.4 10.4 10.5 10.6 10.7 10.8 10.9 11.3 11.3 11.4 11.4 11.9 12.0 12.0 12.0 12.1 12.2 12.2 12.2 12.7 12.7 13.4 13.6 14.0 14.1 14.3 14.5 14.8 15.1 15.2 15.3 15.7 15.9 17.4 17.6 17.8 19.3 20.5 Descriptive Statistics N MEAN MEDIAN TRMEAN STDEV SEMEAN NIELSEN 63 11.176 10.900 11.077 3.586 0.452 MIN MAX Q1 Q3 NIELSEN 4.800 20.500 8.300 13.600 a) Based on the DESCRIBE information, locate and mark the mean and median

Nielsen rating on the sorted data listing above. [No explanation please] b) Is the median an actual value in the data? Why or why not? In two sentences,

explain carefully how the median was calculated from this data set. c) By examining the Nielsen data printed above, explain why the mean is not very

different from the median. d) What is the RANGE for the Nielsen data (single number answer)? e) Calculate (from the DESCRIBE output above) an interval two standard deviations

on either side of the mean? Are about 95 percent of the Nielsen ratings within this interval? Which ratings (if any) are above and below these limits?

f) Write a one-sentence report summarizing to the network programmer your findings about averages and dispersion of new program Nielsen ratings.



3.1: e, 3.2: e, 3.3: c, 3.4: e, 3.5: c, 3.6: d, 3.7: b, 3.8: b, 3.9: b, 3.10: d, 3.11: c, 3.12: e, 3.13: d, 3.65: c; 3.66: d, 3.67: e, 3.80: c, 3.81: e, 3.82: c, 3.83: d, 3.84: d, 3.85: a, 3.86: c, 3.87: e, 3.88: d, 3.89: a, 3.90: b, 3.91.1: a, 3.91.2: b, 3.91.3: c, 3.91.4: d, 3.92.1: d, 3.92.2: a, 3.92.3: a, 3.92.4: d, 3.92.5: d, 3.92.6: c, 3.93: Average beer price in L.A. supermarkets is about $3.65 a six-pack, but prices ranges from as high as $4.29 to as low as $3.29. 3.94: (a) Circle 10.9 for the median and a point between 10.9 and 11.3 on the data listing as the mean; (b) Yes, because n is odd. The (n + 1) / 2st largest (or smallest) observation from the sorted listing is the median. Since (63 + 1) / 2 is 32, the median must be the 32nd largest rating, or 10.9; (c) No extremely large or small ratings occur, nor is there an overabundance of larger ratings not offset by about the same number of lower ratings; (d) Range = Max - Min = 20.5 - 4.8 = 15.7 (e) 95% confidence interval = ( - 2, + 2) = (11.176 - 2(3.586) and 11.176 - 2(3.586)) = (4.00, 8.35), of the n = 63 ratings observed, 61 of the 63 are within this interval, about 97% and close to 95%. None of the show ratings were below the interval, but two were above (19.3 and 20.5); (f) Nielsen ratings for 1993-94 new shows average approximately 11, but ratings ranged from as low slightly less than 5 to one show than exceeded 20.


D. Review Questions for Chapter 4 4.1 By knowing only the trend line, you know all except which one of the

following things about time series data? a. fit around the trend b. steepness of the trend c. location of the trend d. the average rate of increase of the time series data for each time period e. all of the above can be determined from the trend line

4.2 If the trend line for inventories is given by the equation predicted inventory = 50 + 150 Quarter that was fitted from 20 consecutive quarters (1 through 20). The prediction for quarter 21 would be a. forecasting b. extrapolation c. 3200 d. all of the above e. none of the above

4.3 If the trend line for inventories is given by the equation predicted inventory = 50 + 150 Quarter you can predict inventory levels for quarter number 5 to be a. 700 b. 800 c. 900 d. 1000 e. cannot be predicted from the information given

4.4 If the trend line for inventories is given by the equation predicted inventory = 50 + 150 Quarter then inventory levels on average a. rise 600 per year b. rise 200 per quarter c. rise 150 per month d. fall 200 per quarter e. none of the above


4.5 If the trend line for inventories is given by the equation predicted inventory = 50 + 150 Quarter were fit from 20 consecutive quarters (1 through 20), prediction for quarter 21

would be a. forecasting b. extrapolation c. 3200 d. all of the above e. none of the above 4.6 The problem with trend line regressions is that a. eventually all trends must end b. there may not be any trend upward or downward c. they can only apply to time series data d. they do not explain why a trend occurs e. all of the above 4.7 Based on the trend line for sales of a fast growing company given by the

equation predicted sales = 2500 + 500 Year the fitted value of sales for Year 7 is a. 2500 b. 3500 c. 5000 d. 6000 e. cannot be determined from the information given 4.8 Based on the trend line for sales given by the equation predicted sales = 3000 + 600 Year sales on average a. rises 50 per month b. rises 150 per quarter c. rises 600 per year d. all of the above e. none of the above


4.9 A simple regression equation can always be used to predict a dependent variable if

a. the explanatory variable is positive b. the explanatory variable lies within the range of data values c. the explanatory variable has a realistic value d. the predicted value of the dependent variable is realistic e. none of the above

4.10 The intercept in a simple regression equation may always be interpreted as a. the change in the dependent variable for zero change in the explanatory

variable b. the value of the dependent variable when the explanatory variable is zero c. the value we add to b1 X to predict in-range values of the dependent

variable d. the mean of the dependent variable e. all of the above

4.29 If SSE = 200 and SST = 500, then R is equal to a. 60 percent b. 40 percent c. 30 percent d. 20 percent e. none of the above

4.30 The least-squares line has which of the following properties? a. minimizes the sum of errors b. passes through the most points possible c. passes through the origin d. minimizes the SSE e. all of the above

4.31 To determine the standard error of the estimate for simple regression, we divide by n - 2 in the denominator prior to taking the square root because

a. we lose two pieces of information to first determine the error b. we lose two degrees of freedom c. we must first estimate the slope and intercept of the fitted equation d. all of the above e. none of the above


4.32 If SSE = 35 and SST = 140, then R is equal to a. 75 percent b. 60 percent c. 35 percent d. 25 percent e. none of the above 4.33 If R is zero for a regression, then a. the intercept for the regression equation must be zero b. the slope for the regression equation must be zero c. all the fitted values of the dependent variable must be zero d. all of the above e. none of the above 4.34 Calculate R and SEE from the following information: (a) SSE = 120, SST = 1000, n = 25 (b) SSE = 8, SST = 24, n = 33 (c) SSE = 60, SST = 64, n = 65 (d) SSE = 0.4, SST = 1, n = 41 (e) SSE = 44,100, SST = 250,000, n = 22 4.35 Monthly data on short term interest rates for commercial paper from

November 1989 through August 1993 was examined by a financial analyst, using the following variables:

USA Int U.S. short term interest rates (in percent) in month t Month n = 46 months: month = 1, 2, ..., 46 The regression equation is USA Int. = 8.95 - 0.146 Month

[other output not relevant is omitted here]

s = 0.4899 R-sq = 94.2% R-sq(adj) = 94.1% Analysis of Variance SOURCE DF SS MS F p Regression 1 171.69 171.69 715.35 0.000 Error 44 10.56 0.24 Total 45 182.25


(1) The monthly trend rate in short term interest may be described by: Interest

rates (decreased / increased) at an average rate of percentage points per month.

(2) Assuming past trends continued, forecast interest rates for December 1993

(Month = 50): (3) What percent of variation in interest rates is explained by the regression?

%. This percentage may be verified by subtracting from 1 the following ratio: .

(4) The standard error of the estimate, 0.4899, is the square root of which number?

(5) To capture the actual interest rate outcome about 95% of the time, predictions based on the fitted equation may report a margin of error of roughly plus or minus (please round).

(6) The correlation is negative because of the negative sign of the . The correlation coefficient between interest rate and Month is - 0. . [show work]

Answers?


4.43 The mean cross-product deviation for bivariate data are the a. correlation b. coefficient of determination c. standard error of the estimate d. covariance e. none of the above 4.44 Which of the following is a unitless measure ranging from -1 to +1? a. correlation b. coefficient of determination c. standard error of the estimate d. covariance e. all of the above 4.45 Which of the following is not a difference between regression and

correlation? a. correlation requires us to first plot the data b. regression requires that we designate a dependent variable c. regression allows us to make predictions d. correlation is merely a measure of association e. correlation is more appropriate for exploring a new area of inquiry 4.46 If rX,Z = 0 then we say that X and Z are a. uncorrelated b. perfectly correlated c. negatively correlated d. both a and b e. both a and c 4.47 If the correlation among two variables is 0.2, then R for the simple

regression is a. 0.40 b. 0.20 c. 0.04 d. 0.02 e. cannot be calculated with the information given


4.48 If a simple regression has an R of 49 percent, then the correlation between the two variables is

a. 0.2401 b. 0.49 c. 0.07 d. 0.70 e. cannot be calculated from the information given

Answer the next four questions based on the following statistical output: The primary business of a newspaper is to sell readers to advertisers. Data on two variables are collected for Florida newspaper on the following variables: Advert advertisers space (in thousands of inches) purchased during each month Month a time trend variable for each of n = 50 months: month = 1, 2, ..., 50 The regression equation is : advert = 102 0.501 month


S = 7.276 R-sq = 50.7% R-sq(adj) = 49.7% Analysis of Variance SOURCE DF SS MS F p Regression 1 2612.4 2612.4 49.34 0.000 Error 48 2541.4 52.9 Total 49 5153.8 4.49. According to the regression output, advertising space in this newspaper a. Increased at about 102,500 inches per month b. Increased at about 500 inches per month c. Decreased at about 102,500 inches per month d. Decreased at about 500 inches per month e. Cannot be determined from the information provided


4.50. The least-squares equation reduces the total variation in predicting advert a. From 5154 to 2541 b. From 2612 to 52.9 c. From 2541 to 52.9 d. From 50.7 to 49.7 e. From 49 to 48 4.51. We may predict advertising space for month 20 to be approximately a. 92,000 inches with a margin of error of 15,000 inches b. 82,000 inches with a margin of error of 15,000 inches c. 92,000 inches with a margin of error of 7,300 inches d. 82,000 inches with a margin of error of 7,300 inches e. 82,000 inches with a margin of error of 7,300 inches 4.52. The correlation coefficient between advertising space and month was a. +0.71 b. - 0.71 c. +0.26 d. - 0.26 e. Insufficient information to determine answer

4.59 Given that rxy = -.80, determine the following: (a) R for the regression of Y on X and the sign of the slope coefficient b1 (b) R for the regression of X on Y and the sign of the slope coefficient b1


4.60 The following multiple regression determines insurance charged to short haul trucking firms: premium = b0 + b1 fleetsz + b2 popden

where the variables in the regression equation are defined as: premium = insurance premiums charged each firm (in dollars per truck) fleetsz = number of truck owned by each firm popden = county population density (people / square mile) where

company is located From a random sample of n = 32 trucking firms surveyed in 1993, the regression equation is premium = 779 - 5.49 fleetsz + 0.885 popden


S = 332.5 R-sq = 36.6% R-sq(adj) = 32.2%

Analysis of Variance SOURCE DF SS MS F p Regression 2 1850413 925206 8.37 0.001 Error 29 3206046 110553 Total 31 5056459

1. This data set consists of time series / cross section (circle one) data. 2. This is multivariate regression because there is more than one variable. 3. The statistic tells us we have explained over one-third the variation in

premiums. 4. The degrees of freedom for the error sum of squares = , found by _. 5. Use the fitted equation to predict premiums for a firm with 10 trucks in a county

with 50 people / square mile. [round answer to the nearest dollar] 6. For the following, show computations assuming no other explanatory variable

changes: (a) Companies increasing fleet size 20 trucks are charged $110 lower premiums on

average. b1 fleetsz = (b) Companies moving to counties of 200 fewer people / square mile are charged

$177 less on average. b2 popden = Answers?


4.72 Multiple regression means that a. we run more than one regression equation b. we run the same regression equation more than once c. we have more than one dependent variable d. we have more than one explanatory variable e. none of the above 4.73 When one regression equation contains an additional explanatory variable

not present in a second, the first equation will nearly always have a a. higher adjusted R b. lower adjusted R c. higher R d. lower R e. both R and adjusted R may be higher or lower depending on the data For each of the following four questions, assume that the regression equation for

the apartment rent example is Rent = - 200 + 1.0 Size - 10 Walk 4.74 The estimate of monthly rent for an 700 square foot apartment that is a 20

minute walk from campus is a. $200 b. $300 c. $400 d. $500 e. cannot be calculated from the information given

4.75 How much should you expect rents to change on average if you moved to the same-sized apartment, but 7.5 minutes further walking distance from campus?

a. $15 less b. $15 more c. $75 less d. $75 more e. exactly the same amount


4.76 The monthly rent for a 1200 square foot apartment that is a 2 minute walk from campus may be estimated to be

a. $1180 b. $980 c. $1220 d. $1420 e. $760 4.77 How much should you expect rents to change on average if you moved to an

equal-sized apartments 10 minutes further walking distance from campus? a. $100 less b. $100 more c. $20 more d. $200 more e. exactly the same amount 4.78 We should not expect R from two regressions to be directly comparable if a. the samples for the two regressions was gathered from very different time

periods b. the sample for the one of regressions was from a more broadly-defined

population c. the dependent variables used in each regression was defined differently d. all of the above e. none of the above 4.79 Suppose a particular regression equation is utterly worthless in accounting

for variation in the dependent variable over the entire population. Then we should expect that the least-squares equation from a random sample of that population will yield an R = 0

a. only very rarely b. less than 50 percent of the time c. most of the time d. nearly always e. always


4.80 Which is not true about the difference between R and the adjusted R? a. the difference is greater for smaller sample sizes b. the difference is greater if R is large c. the difference is greater if there are more explanatory variables in the

equation d. adjusted R cannot be greater than R e. adjusted R cannot be greater than 100 percent 4.81 Multiple regression is so often used in business and economics today

because a. most variables we seek to explain are affected by a complex set of factors. b. an acceptable fit often cannot be obtained with only a single explanatory

variable. c. controlled experiments are often too difficult to conduct. d. the abundance of data and speed of modern computers make multiple

regression a practical option. e. all of the above.

4.82 In comparing regression fits on cross section and time series data

a. R is usually lower for cross section data because it is easier to explain why different items are different

b. R is usually higher for cross section data because it is easier to explain why different items are different

c. R is usually lower for cross section data because it is more difficult to explain why different items are different

d. R is usually higher for cross section data because it is more difficult to explain why different items are different

e. there is no systematic difference between fits for either type of data Answers? 4.72-4.82


Answer the next five questions based on the following case description and statistical output:

We next examine a regression equation where advertising space is a function of newspaper sales and the state of the economy:

advert = advertising space (in thousands of inches) purchased during each circ = the monthly level of circulation (measured in millions)

jobless = the monthly unemployment rate (in percent)

The regression equation is:

advert = 125 + 1.95 circ - 6.13 jobless 4.83 Forecast advertising space next month when circulation is 4 million and

unemployment rate is 6 percent. a. 22,000 inches b. 29,000 inches c. 96,000 inches d. 132,000 inches e. None of the above 4.84 If the circulation numbers were instead reported in thousands (rather than

millions) of newspapers, what would the coefficient of circ now have to be for the fitted equation to tell exactly the same story?

a. 1950 b. 1.95 c. 0.00195 d. 0.00000195 e. Cannot be determined from the information provided. 4.85 Assuming unemployment is the same, circulation decline of one million will

result in a a. 1950 inch increase in advertising space b. 127,000 inch increase in advertising space c. 1950 inch decrease in advertising space d. 127,000 inch decrease in advertising space e. None of the above


4.86 For a one percentage point increase in the unemployment, other things equal, advertising space will

a. increase by about six thousand inches b. increase by about 119 thousand inches c. decrease by about six thousand inches d. decrease by about 119 thousand inches e. none of the above 4.87 Which of the following describes the data set and regression equation: a. data set is time series data and the regression is multivariate regression b. data set is cross section data and the regression is multivariate regression c. data set is time series data and the regression is simple regression d. data set is cross section data and the regression is simple regression e. not enough information provided to determine the data set and regression

type. 4.88 Determine for each of the following cases: (a) b1 = 15, X = 10 (b) b1 = 15, X = 100 (c) b1 = 1.5, X = 100 (d) b1 = -5, X = 10 (e) b1 = 15, X = -10


4.88 Answer the next four questions based on the following case and statistical output on the regression: Predicted P GAS = b0 + b1 month

where the variables are:

P GAS monthly average price at pump for regular gasoline (in cents / gallon) month numbered from 1 to 53 from April 1986 to August 1990.

The Minitab regression equation is: P GAS = 83.8 + 0.414 month


S = 4.532 R-sq = 66.9% R-sq(adj) = 66.3%

a. Rounded to the nearest cent, the annual trend rate (i.e., every 12 months) in gas price increases is about

a. 1 cent b. 5 cents c. 84 cents d. 89 cents e. None of the above

b. The forecast of gas prices in March 1991 (i.e., month = 60), assuming past trends continue is approximately

a. 25 cents b. 35 cents c. 84 cents d. 109 cents e. None of the above

c. The variation in gas prices explained by this trend equation is approximately what fraction?

a. One third b. One half c. Two thirds d. Three quarters e. Cannot be determined from the output above

d. The correlation between gas price and month is a. 0.44 b. 0.66 c. 0.67 d. 0.82 e. Insufficient information provided to determine the answer


4.89 Answer the next four questions based on the following case and statistical

output: Data on the following fours variables were collected from a random sample of n=49 persons taking the business law section of the CPA (Certified Public Accounting) exam:

LAWSCORE = each person's score on the business law section of the CPA exam HOURS = number of hours that person studied per week to prepare for the exam GPA = undergraduate grade point average of the person taking the exam WORKEXP = number of years work experience of the person taking the exam

The regression equation is in the following form: Predicted LAWSCORE = b0 + b1 HOURS + b2 GPA + b3 WORKEXP

When the regression was run, the following output results: LAWSCORE = 53.8 + 0.400 HOURS + 3.45 GPA + 0.272 WORKEXP


s = 9.050 R-sq = 25.4% R-sq(adj) = 20.5%

Analysis of Variance SOURCE DF SS MS F p Regression 3 1256.46 418.82 5.11 0.004 Error 45 3685.78 81.91 Total 48 4942.25

a) The degrees of freedom for the error sum of squares are calculated as follows: a. 48 - 1 - 1 = 46 degrees of freedom b. 50 - 2 = 48 degrees of freedom c. 45 - 4 = 41 degrees of freedom d. 49 - 3 - 1 = 45 degrees of freedom e. None of the above

b) If a second regression equation reports an R2 = 28.6% and an adjusted R2 =19.2%, then this second equation has

a. A better fit than the regression equation above. b. A worse fit than the regression equation above. c. The same fit as the regression equation above. d. Not enough information provided to answer this question.


c) Assuming the other explanatory variables don't change, ten more hours study weekly

a. increases exam scores an average of 0.4 points b. increases exam scores an average of 4 points c. increases exam scores an average of 40 points d. increases exam scores an average of 58 points e. None of the above d) The exam score for a person studying 30 hours per week who earned a 3.0

grade point average in college and has ten years work experience is predicted to be approximately

a. 72 b. 79 c. 85 d. 91 e. None of these Answers? 4.90 At the beginning of 1991, a national realtors association wants you to analyze trends in the home construction industry over the preceding four years and forecast new construction activity this year. Predicted H starts = b0 + b1 Month The variables in the regression equation are for month t H starts number of housing starts (in thousands) during month t Month month = 1 to 48 from January 1987 to December 1990) The regression is fit yielding the following Minitab output: The regression equation is: H starts = 1727 - 12.2 month

[other output not relevant is omitted here] s = 97.54 R-sq = 75.7% R-sq(adj) = 75.2% Analysis of Variance SOURCE DF SS MS F p Regression 1 1366204 1366204 143.60 0.000 Error 46 437648 9514 Total 47 1803852 Now answer the following 10 questions:


a) What was the monthly trend rate in housing starts over the period examined? Housing starts (increased / decreased) at an average rate of thousand per

month decreased, 12.2 b) What percent of variation in car sales was explained by this trend equation?

75.7% c) Calculate the correlation between Month and Sales.

r = 2R =

757.0= - .87 because b1


- - ** 1750+ * - * * * H strts - ***** * - * 2 *** * - **2 * * 1400+ ** * * ** * - ** * * * - * * - **** - 2 * *** 1050+ * **2 - * *** - * - * - --+---------+---------+---------+---------+---------+----month 0 12 24 36 48 60

i) Based on your examination of this plot, discuss how you can tell that the regression equation we estimated would yield very bad forecasts for mid- and late-1991 (months 54 to 60).

The downward trend over the first four years (48 months) was used to fit the regression equation. However, the trend may have reversed and turned into an upward trend thereafter. Thus, forecasts from the fitted line will be increasingly wrong and too low.

j) If a different regression equation were to be used instead of a time trend equation, suggest one or more explanatory variables that would explain the variation in housing starts in the U.S. Acceptable answers: interest rates, construction costs, unemployment, and population.

Answers?


4.91 The director of a hospital pharmacy wants to determine how staffing level affects the rate at which prescriptions are processed. She decides to use the following regression equation: prescript = b0 + bb staff + b2 in-pat where the variables are defined as follows: staff = average number of staff on duty on day t presrip = prescriptions processed per hour during day t in-pat = number of in-patients at the hospital on day t Forty-seven days are sampled and a regression yields the following equation: prescrip = - 67.1 + 21.0 staff + 0.395 in-pat.


S = 14.22 R-sq = 69.6% R-sq(adj) = 68.3% Analysis of Variance SOURCE DF SS MS F p Regression 2 20392 10196 50.45 0.000 Error 44 8892 202 Total 46 29284 a) Verify that the error degrees of freedom should be 44, given this regression and

sample size. DF = n - k - 1 = 47 - 2 - 1 = 44

Using the marginal effects"delta" () formula answer b and c: Based on the fitted equation, determine the expected change in the prescription processing rate, assuming the other explanatory variable in the regression equation does not change: [In each case, show delta formula computations and report answers in correct direction of change, numerical magnitude, and correct units] b) The staff level at the pharmacy is increased by two persons. prescrip = b1 staff = (+21)(+2) =+42 an increase of 42 prescriptions /

hour c) The number of patients at the hospital decreases by 100. prescrip = b2 in-pat = (+.395)(-100) =-39.5 a decrease of 40

prescriptions / hour Make a prediction for questions d and e: d) Predict the prescription processing rate when there are 200 patients in the

hospital and 10 persons maintained on staff at the pharmacy. predicted prescrip = -67.1 + 21.0(10) +.395(200) = -67.1 + 210 + 79 = 222 prescriptions / hour


e) Why shouldn't you worry about the negatively signed intercept term, -67.1, in the fitted equation? [Hint: use information from the descriptive statistics below]

Even if both variables are at their minimum values, predicted prescrip would still have positive value. N MEAN MEDIAN TRMEAN STDEV SEMEAN staff 47 9.512 9.563 9.509 1.037 0.151 prescrip 47 170.55 174.93 170.68 25.23 3.68 in-pat. 47 95.98 97.00 95.72 15.40 2.25 MIN MAX Q1 Q3 staff 7.375 12.125 8.625 10.187 prescrip 110.00 227.86 153.57 188.14 in-pat. 72.00 129.00 81.00 108.00 f) What is the danger of using the fitted equation to predict "prescript" if only four

staffers are on duty at the pharmacy? The range of staff data was 7.375 to 12.125, so four staff would result in

extrapolation if used to fit the regression and predictions cannot be trusted. Answers?

Answers for Chapter 4 4.1: a; 4.2: d; 4.3: b; 4.4: a; 4.5: d; 4.6: e; 4.7: d; 4.8: d; 4.9: b; 4.10: c; 4.29: a; 4.30: d; 4.31: d;

4.32: a; 4.33: b; 4.34 (rounded): a) 88%, b) 67%, c) 6%, d) 60%, e) 82%; 4.35; 4.43: d; 4.44: a; 4.45: a; 4.46: a; 4.47: c; 4.48: e; 4.49: d; 4.50: a; 4.51: a; 4.52: b; 4.59: a and b are the same

answer (64% and negative sign); 4.60; 4.72-4.82; 4.88: a) +150, b) +1500, c) +15, d) -50, e) -150; 4.89; 4.90; 4.91;


E. Review Questions for Chapter 5

5.1 Which of the following variables would best measure the quality of education offered among a population of colleges?

a. SAT exam scores of entering students at each college b. salaries of professors at each college c. average grades of all graduates at each college d. satisfaction surveys for graduates of each college e. the tuition costs at each college 5.2 When making decisions based on time series data, one rule of advice is a. base your decisions only on the most recent data available b. don't be too quick to proclaim success or failure of a new policy c. we must learn the lessons of history so that we never risk repeating past

mistakes d. the behavior of people in each age group today can be used to predict the

behavior of those same age groups in the future e. time series data are superior to cross section data for decision making 5.3 What is wrong with deciding whether a business has grown over the past

twenty years by comparing the sales revenues? a. the variable is contaminated by price changes from inflation b. this involves circular reasoning c. sales revenue usually cannot be measured d. sales revenue is not a variable e. there is nothing wrong 5.4 Which of the following is not an example of faulty reasoning involving time? a. A firm suffering a temporary cash flow crisis fires a large portion of its

workforce. b. Things were better in the good old days, so we should do things the way they

used to be done. c. Luxury car sales increased in the 1980s because of ads using 1960s rock music,

so the same music is approved for ad campaigns in the 1990. d. all of the above



5.5 A business school accreditation organization circulates class evaluation forms to students attending the next to the final week of the term. All except one of the following would likely cause bias in estimating educational effectiveness of the courses:

(a) students place too much faith on instructors who say the courses are effective.

(b) students underestimate the usefulness of courses until they obtain full time jobs in business.

(c) the evaluation forms contain questions primarily focused on whether courses meet minimum standards.

(d) students who dropped or withdrew from the course before the final week are not sampled.

(e) all of the above are likely sources of bias.

5.6 A state in fiscal crisis is considering various tax reform proposals. To get a feeling for what voters would support, the governor decides to conduct a survey before deciding which reforms to propose to the state legislature. Which of the following survey designs would you recommend?

(a) set up a series of 900 numbers for people to call to express their preference.

(b) mail a survey form to all registered voters, and determine the preferences from those who respond.

(c) conduct extensive "man-on-the-street" interviews at all major shopping malls.

(d) survey a random sample of political science professors and other expert as to which reform plan they believe the voters will support.


5.1: d, 5.2: b, 5.3: a, 5.4: d, 5.5: e, 5.6: e.


F. Review Questions for Chapter 6

6.1 A personnel manager uses insight gathered from experience and training to

quantify the probability that a new salesperson will be caught stealing. The

approach used to arrive at this probability is best described as the

a. frequency approach

b. subjective approach

c. classical approach

d. probability approach


6.2 If the set S is defined by S = {Toyota Corolla, Nissan Sentra, Honda Civic,

Mazda MPV Minivan, Ford trucks}, which of the following dealerships could

have its new vehicle inventory described by S?

a. a Japanese car dealer

b. a foreign car dealer

c. a car dealer

d. a car, truck, and van dealer

e. each of the above

6.3 An insurance agent calculates that one in twenty unsolicited letters to

prospective clients results in a new policy sold. What is the probability that

any given letter will yield a sale?

a. 0.95

b. 0.50

c. 0.20

d. 0.05

e. insufficient information answer

6.4 Subjective probability

a. is derived from human judgments.

b. expresses our personal degree of belief.

c. is small when there is great doubt that an event will occur.

d. is most appropriate in new, complex, and difficult to quantify situations.

e. all of the above.


6.16 If the probability of an event A is P(A) = .25, then the probability of its complement C, P(C) must be

a. 0 b. 0.25 c. 0.5 d. 0.75 e. 1.0 6.17 If this year, P(Recession) = 0.25, P(Mideast War) = 0.10, and P(Recession and Mideast War) = 0.05, then P(Recession or Mideast War) is

a. 0.025 b. 0.20 c. 0.30 d. 0.35 e. 0.40

6.18 Upon entering an intersection where two roads cross, cars have a 0.2

probability of turning left. Then the event Right Turn a. has a probability of 0.8 b. is the complementary event of Left Turn c. is mutually exclusive of Left Turn d. is independent of Left Turn e. all of the above

6.19 Suppose that of all newly-trained employees at a fast-food franchise, fifty percent are still working there one year later but another thirty percent do not last more than the first two months. Therefore, there is a twenty percent chance that a new employee will

a. be around after two months b. not last a year c. be fired immediately d. work there more than two months but no more than a year e. insufficient information to answer


6.20 A new product of the type your company is considering have achieved market success in 200 out of 1000 cases. Which of the following correctly describes this record?

a. the probability of success is 0.20 b. the probability of not achieving success is 80 percent c. the odds are four-to-one against success d. the chance of success is one in five e. all of the above

6.21 If there are even odds that you will get a job offer from Acme, Inc., then the probability P(Acme job offer) equals

a. 100 percent b. 75 percent c. 50 percent d. 33 percent e. not enough information provided

6.22 Which of the following does not indicate statistical independence among events?

a. Students in the honors program have the same chance of passing this course as any other type of student.

b. The chance of a small firm failing is identical to that for any size firm. c. The odds of the boss' son getting a promotion are no better or worse than

for any other employee of the firm d. People who saw their new commercial were no more likely to shop at K-

Mart than those who didn't watch it. e. All of the above indicate independent events.

6.23 For a product to be delivered on time, all of the following must occur: the order is processed within one work day, the product is shipped the following day, and the shipment is routed through the proper regional distribution center. If each of these event are independent and their probabilities are 0.8, 0.8, and 0.5, the probability of on-time delivery is a. 0.50 b. 0.48 c. 0.40 d. 0.32 e. 0.24


6.24 If S is the set containing events describing the time between servicing of a copying machine under warranty, which of the following would be a possible event in S? a. five months b. customer complained c. asked for money back d. cartridge need replacing e. all of the above

6.25 If events S = {A, B, C} is an exhaustive set of events, then a. P(A) + P(B) + P(C) = 1 b. P(S) = 1 c. A, B, and C must be mutually exclusive events d. all of the above e. none of the above

6.26 If S = {A, B, C} and P(A) + P(B) + P(C) = 1.0, then a. A, B, and C are mutually exclusive and exhaustive events. b. A, B, and C are mutually exclusive but not exhaustive events. c. A, B, and C are exhaustive but not mutually exclusive events. d. A, B, and C are complements. e. A, B, and C are independent events.

6.27 If the sample space consists of a listing of each product sold at a supermarket, then frozen foods and fresh produce are

a. outcomes b. events c. sample spaces d. experiments e. none of the above

6.28 If the sample space consists of a listing of each product sold at a supermarket, then frozen foods and fresh produce are

a. independent b. mutually exclusive c. exhaustive d. complementary e. all of the above


6.29 Getting promoted to a senior vice-president position has a probability of 0.50 if you are head of the marketing but only 0.20 if you are head of research. These are examples of

a. marginal probabilities b. joint probabilities c. conditional probabilities d. independent probabilities e. none of the above

6.30 Which of the following sets consists of mutually exclusive events? a. Marital Status = {single, married, divorced, widowed} b. Education = {high school degree, college degree} c. Region = {South, West, East, North} d. Occupation = {office worker, clerk, receptionist} e. none of the above

6.31 If events A and B are statistically independent, and P(A) = 0.5 and P(B) = 0.2, then the joint probability P(A and B) must be

a. 0.1 b. 0.2 c. 0.5 d. 0.9 e. cannot calculate without knowing the conditional probabilities

U.S. manufacturers are surveyed about whether they have fewer than 50 workers and if they do any exporting of their product. Answer the following questions based on the Venn Diagram:

E x p o r t

L e s s t h a n 5 0 W o r k e r s

U . S . M a n u f a c t u r i n g C o m p a n i e s


6.32 Which of the following is described in the Venn diagram? a. Exporting has a greater probability than Less Than 50 Workers b. Less Than 50 Workers has a greater probability than At Least 50 Workers. c. At Least 50 Workers has a greater probability than Not Exporting. d. All of the above are portrayed in the diagram. e. Cannot be answered by examining the diagram.

6.33 Which of the following are described in the Venn diagram?

a. Exporting and Less Than 50 Workers are exhaustive events. b. Exporting and Less Than 50 Workers are mutually exclusive events. c. Exporting and Less Than 50 Workers are complementary events. d. All of the above e. None of the above

6.34 Which of the following conditional probabilities is most closely approximated in the Venn diagram above.

a. P(Exports | Less Than 50 Workers) is 0.50 b. P(Less Than 50 Workers | Exports) is 0.50 c. P(Exports | Less Than 50 Workers) is 0.85 d. P(Less Than 50 Workers | Exports) is 0.85 e. Cannot be answered with information presented in the diagram.

6.35 A new comedy series has a 20 percent chance of being renewed for a second season. On average, 60 percent of second-season comedies are renewed. What is the probability a new comedy will still be on the air for its third season?

a. 0.48 b. 0.32 c. 0.12 d. 0.08 e. cannot be determined from the information given

6.36 If events A and B are statistically independent, then a. P(A) = P(B) b. P(A) + P(B) = 1 c. P(A|B) = P(A) d. P(A|B) = P(B) e. all of the above


6.37 Which of the following pairs of events are most likely to be independent? a. a rusting fender and a car less than two years old b. a person who has attended college and an athlete over 7 feet tall c. a company president earning more than $500,000 a year and a Fortune

500 company d. an A on the first exam and final course grade of D e. having blue eyes and majoring in accounting

6.38 If the probability of an event A is P(A) = .25, then the probability of its

complement C, P(C) must be a. 0 b. 0.25 c. 0.5 d. 0.75 e. 1.0

6.39 People usually express reluctance to offer a needy relative one of their two kidneys for transplant surgery. They are often convinced to become donors when they learn that the same diseases that cause one kidney to fail will also damage the other kidney. This argument relies on explaining that the failure of each kidney are not a. exhaustive events b. mutually exclusive events c. independent events d. complementary events e. all of the above 6.40 If events A and B are statistically independent, and P(A) = 0.5 and P(B) = 0.4,

then the joint probability P(A and B) must be a. 0.1 b. 0.2 c. 0.5 d. 0.9 e. cannot calculate without knowing the conditional probabilities


6.41 For a product to be delivered on time, all of the following must occur: the order is processed within one work day, the product is shipped the following day, and the shipment is routed through the proper regional distribution center. If each of these event are independent and their probabilities are 0.8, 0.6, and 0.5, the probability of on-time delivery is

a. 0.50 b. 0.48 c. 0.40 d. 0.30 e. 0.24

6.64 If X is a random variable with sample space {2, 6} and P(X=2) = 0.5, P(X=6) = 0.5, then 4 equals

a. the mean b. the variance c. the standard deviation d. both a and b e. both a and c

6.65 In Tampa, the probability distribution for the random variable X measuring the price charged for weekday video tape rental is found to be:

Price Charged P(X) $ 1.50 0.10 2.00 0.60 2.50 0.10 3.00 0.20

For a randomly selected video store, the probability P($1.00


6.69 A manager may not select the investment alternative with the highest expected profit if another investment

a. has a lower standard deviation and the manager is averse to risk b. has a higher standard deviation and the manager is averse to risk c. has a lower standard deviation and the manager is risk loving d. both a and c are possible explanations of the manager's behavior e. both b and c are possible explanations of the manager's behavior

The questions that follow are related to the following decision making problem: A manufacturer has to decide whether to replace (R), fix (F), or ignore (I) its aging factory equipment this year. If R is chosen, there is a 0.8 chance of no production stoppages (NO) and a 0.2 chance of minor stoppages (MIN). If F is selected, on the other hand, P(NO) falls to 0.5 and P(MIN) increases to 0.5. If I is chosen by the manufacturer, P(MIN) = 0.6 and there is now a 0.4 chance for major stoppages (MAJ). Because of the higher costs associated with replacing equipment, profits from choice R will only be 15 if NO occurs and 5 if MIN results. For choice F, a NO outcome yields profits of 18 and MIN results in profits of 8. In the case of choice I, MIN produces profits of 20 but MAJ cause profits of 0.

6.70 The number of decision forks faced by this manufacturer is

a. 0 b. 1 c. 2 d. 3 e. 4

6.71 The number of chance forks faced by this manufacturer is

a. 0 b. 1 c. 2 d. 3 e. 4


6.72 The greatest expected profits for this manufacturer are derived by choosing

a. R b. F c. I d. either a or b e. either b or c

6.73 The expected profits from R is while expected profits from I are

a. 7 and 8 b. 7 and 12 c. 13 and 8 d. 13 and 12 e. none of the above

6.74 In problems using Bayes' theorem, we

a. always seek to determine a conditional probability as our answer b. assume that outcomes each statistically independent c. look for keywords such as "who", "what", and "how" to determine

whether we are dealing with marginal probabilities d. all of the above

e. none of the above 6.75 In problems using Bayes' theorem, we

a. always seek to determine a conditional probability as our answer b. assume that events are not statistically independent c. look for the presence of keywords such as "given that", "if", and "when" to

identify conditional probabilities d. all of the above e. none of the above


Use the information from the following situation to answer questions below: A study of past shuttle launch attempts reveals that the probability of a launch (L) taking place was 40 percent if a heavy clouds cover (HC) was forecast, 60 percent if a light cloud cover (LC) was forecast, and 80 percent if no clouds (NC) were forecast. A survey of weather forecasts for the Cape informs us that clear days are forecast three-quarters of the time and light clouds are forecast 20 percent of the time. Assume that there are only three kinds of forecasts: HC, LC, and NC.

6.76 The probability P(HC) is a. 0 percent b. 5 percent c. 30 percent d. 37.5 percent e. 55 percent

6.77 The 40, 60, and 80 percent probabilities given in the problem are a. marginal probabilities b. conditional probabilities c. joint probabilities d. Bayesian probabilities e. all of the above

6.78 Using Bayes' theorem, we may use the shuttle launch and weather information to solve for a. P(HCL)

b. P(LCL) c. P(NCL)

d. all of the above e. none of the above

6.79 The denominator 0.74 in Bayes' formula from the launch and weather probabilities is calculated from the following sum: a. 0.01 + 0.24 + 0.49 b. 0.02 + 0.12 + 0.60 c. 0.04 + 0.08 + 0.62 d. 0.12 + 0.24 + 0.38 e. 0.20 + 0.30 + 0.24


6.80 The probability that heavy clouds were forecast if a launch is known to have occurred that day is approximately

a. 22 percent b. 12 percent c. 7 percent d. 3 percent e. 1 percent


6.1: b; 6.2:d; 6.3:d; 6.4: e; 6.16: d; 6.17: c; 6.18: c; 6.19: d; 6.20:e; 6.21:d; 6.22:e; 6.23: d; 6.24: a; 6.25:b ; 6.26:a; 6.27:b; 6.28:b; 6.29: c; 6.30: e; 6.31:a; 6.32: b; 6.33: e; 6.34:b; 6.35: c; 6.36:c; 6.37:e; 6.38:d; 6.39:c; 6.40:b; 6.41:e; 6.64: d; 6.65:d; 6.69:a; 6.70: b; 6.71:d; 6.72:d; 6.73: d; 6.74:a; 6.75:d; 6.76: b; 6.77: b; 6.78:d; 6.79:b; 6.80: d


G. Review Questions for Chapter 7

7.1 Which of the following is not a method to determine the appropriate distribution for a decision making problem?

a. make reasonable assumptions about the distribution in the population b. apply well-understood distributions as approximations for large-sample

situations c. apply well-understood distributions by using ordinal measures d. discern the population distribution from the sample's distribution in large

sample situations e. all of the above are valid methods

7.2 In many situations, we may be able to assign a distribution for our analysis by a. examining distributions of earlier studies b. asking experts about the process by which the data are generated c. using our subjective feeling d. all of the above e. none of the above

7.3 Most statistical analysis uses only a few distributions for all but one of the following reasons:

a. we may use large sample properties b. business variables are distributed in only a few different manners c. we can represent many distributions by a handful of distribution families d. business statistics relies primarily on discrete distributions e. all of the above are explanations

7.4 In distributions that are skewed to the right, a. the median will lie to the left of the mean b. the mean will lie to the left of the median c. the median and mean will be identical d. the relationship between the median and mean will depend on the specific

distribution e. skewed distributions do not have a median


7.5 The probability that exactly two computers in the lab will break down this month is approximately

a. 0.1 b. 0.2 c. 0.3 d. 0.4 e. 0.5 7.6 The probability that no more than two computers will break down this

month is approximately a. 0.3 b. 0.4 c. 0.5 d. 0.6 e. 0.7 7.7 If the cost of repairing a computer is $300, the approximate probability that

service to the lab will cost the maintenance firm at least $1800 is a. 0.001 b. 0.006 c. 0.01 d. 0.06 e. 0.1 7.8 Which of the following is not an example of a Bernoulli trial: a. the merger goes through or it does not go through b. the manager hired is a male or a female c. the sale takes place before or after lunch d. the stock market goes up today or it does not go up e. all of these are examples of a Bernoulli trial

7.9 A company either adopts TQM methods or it does not adopt them. If the probability of adoption is 0.4, then, in the notation of Bernoulli trials,

a. P(S) = 0.4 b. P(F) = 0.6 c. p = 0.6 d. q = 0.4 e. all of the above


7.10 If the probability of any particular car buyer choosing the dealer's bank financing is 0.7, then the probability that the next four buyers will each choose the dealer's bank financing is approximately

a. 0.53 b. 0.49 c. 0.34 d. 0.24 e. 0.17

7.11 For the preceding example, out of n = 5 buyers the expected number of buyers who accept the dealer's bank financing is

a. 0.7 b. 1.05 c. 2.5 d. 3.2 e. 3.5

7.12 The standard deviation for the expected number of buyers in the preceding example is

a. 3.50 b. 1.87 c. 1.22 d. 1.05 e. 1.02 7.13 A probability density function applies only to a. continuous random variables b. discrete random variables c. distributions having both tails infinitely long d. distributions having at least one infinitely-long tail e. any random variables

7.14 By examining the algebraic function for the normal pdf, it is easy to see that the density

a. is determined from only two parameters, and b. is the same for x = 1.5 as it is for x = 1.5 c. always has a positive value d. is a maximum at x = e. all of the above


7.15 Which of the following is not a characteristic of the normal pdf? a. it is unimodal b. it is symmetrical c. the mean and mode are identical d. the mean and median are identical e. all of the above are characteristics of the normal pdf 7.16 Which of the following would be most likely to be approximately normal? a. the distribution of annual income of U.S. households b. distribution of city and town populations in Texas c. age distribution of workers at Kodak d. number of McDonalds franchises in each of the fifty states e. sales of manufacturing corporations in the United States 7.17 Which of the following is true about the standard normal distribution: a. the mean is 0 b. the standard deviation is 1 c. the variance is 1 d. all of the above e. a and b only 7.18 Ninety-five percent of the area under the normal pdf is a. within 1.96 standard deviations of the mean b. within 1.96 of the mean c. within 1.96 of zero d. beyond 1.96 of zero e. none of the above 7.19 If class size at a college is normally distributed, approximately 68 percent of

the class sizes at the college are a. within one standard deviation of zero b. within one student of the mean c. within one percent of the mean d. within one standard deviations of the mean e. within one student of the standard deviation


7.20 If class size at a college is normally distributed, then approximately 95 percent of the class sizes at the college are

a. within two standard deviation of zero b. within two student of the mean c. within two percent of the mean d. within two standard deviations of the mean e. within two student of the standard deviation 7.21 A hardware store has weekly sales that are normally distributed with mean

of $18,000 and standard deviation of $4,500. What can you conclude about the median and modal class midpoint, and approximate percentage of weeks with sales between $9,000 and $27,000?

7.22 A quality control chart records the lead impurity levels for 60 motor oil

samples collected today. From years of operation, the production manager knows that impurity levels for properly functioning machinery are normally distributed with mean of 80 parts per million (ppm) lead impurities and standard deviation of 12 ppm.

a) What can you conclude about the median and mode for this distribution? b) What is an interval of lead impurity levels wide enough to include approximately

57 (or 95 percent) of the 60 oil samples? c) What is an interval of impurity levels wide enough to include virtually all 60

(about 99.5 percent) of the samples? d) How many standard deviations from the mean would an impurity level of 140

ppm be? e) How many standard deviations from the mean would an impurity level of 62

ppm be? f) To standardize the impurity data to a standard normal variable Z, you would

subtract the number from each value and then divide by the number _______. By doing so, the new data Z would have a mean equal to and a standard deviation equal to .



7.1: e; 7.2: d; 7.3: d; 7.4: a; 7.5:c; 7.6: e; 7.7: b; 7.8: e; 7.9: e; 7.10:d; 7.11: e; 7.12: e; 7.13: a; 7.14: e; 7.15: e; 7.16: c; .17: d; 7.18: a; 7.19: d; 7.20: d; 7.21: Average sale, whether measured by the mean, median, or mode, should be about $18,000 per week because the distribution is normal. Approximately 95 percent of the weeks should experience sales between $9,000 and $27,000 because 95% of the population for a normally distributed variable should have values within two standard deviations (2 times $4,500) of the mean, $18,000; 7.22: a) median and mode will be the same as the mean, 80 ppm, b) plus or minus 2 is 80 24, or an interval of (56 ppm, 104 ppm), c) plus or minus 3 is 80 36, or an interval of (44 ppm, 116 ppm), d) (140 - 80)/12 = 5 standard deviations above the mean, e) (62 - 80)/12 = -18/12 = -1.5 standard deviations above the mean, f) 80, 12,zero, 1.


H. Review Questions for Chapter 8 8.1 Statistical inference favors the use of larger samples because large sample

size do each of the following except: a. reduce the thickness of the t distribution tails.

b. increase the n

quotient in the standard error calculations. c. tend to make central limit theorem approximations appropriate. d. permit the use of the normal distribution for our sampling distribution. e. all of the above 8.2 If X is a normally distributed random variable with mean and standard

deviation , then X will be a random variable with a. a normal distribution b. a mean of

c. a standard deviation of /n

d. all of the above e. none of the above

8.3 If X is a random variable, the sampling distribution of X

a. is normally distributed if X is normal with a known value of b. has a t distribution if X is normal and unknown c. is approximately normal for large samples and known value of d. has a t distribution approximately for large samples and unknown e. all of the above 8.4 Which of the following are not common characteristics of both the normal

distribution and t distributions: a. Their shape depends on the number of degrees of freedom. b. They are symmetrical. c. Each have two infinitely-long tails. d. They each have a single mode. e. All of the above are characteristics of both distributions.


8.5 If mean auto sales for a random sample of n = 9 salespersons last year was $300,000 and the sample standard deviation was $90,000, then we should use as the standard error of the estimate a value of

a. $60,000 b. $30,000 c. $15,000 d. $7500 e. answer depends on the choice of sampling distribution.

8.6 If = 8 for a random variable X, then X for a sample size of 16 is a. 0.5 b. 2 c. 4 d. 8 e. 32

8.7 If s = 24 for a random sample, then s X for a sample size of 36 is a. 0.67 b. 3 c. 4 d. 8 e. 144

8.8 In comparing the t and standard normal Z distributions, which of the following is not true?

a. the t distribution is not symmetrical for small samples b. the t distribution converges to the normal distribution as the sample size

increases c. the t distribution has thicker tails than the normal d. only the t distribution varies with the number of degrees of freedom e. all of the above are true 8.9 The central limit theorem is applied to inference situations where a. the sample size is large b. the sample size is small c. the population is normally distributed d. the sample is not a random sample e. the population standard deviation is unknown


8.31 The difference between a parameter and a sample point estimate of that parameter is called the

a. sampling error b. bias c. variance d. distribution e. degrees of freedom

8.32 Which of the following does not suggest an interval estimate for the population mean:

a. As a rough guess, I'd say we rework an average of 15 assemblies each month.

b. Our new boss reprimands a dozen or so employees a week. c. Flights average 10 minutes late give or take five minutes. d. GM's market share averaged about 40 % in each of the past three decades. e. All of the above suggest interval estimates.

8.33 Which of the following does not involve statistical inference? a. descriptive statistics b. point estimation c. interval estimation d. hypothesis testing e. forecasting

8.34 Which information is generally found in a confidence interval? a. a point estimate b. an interval width c. a confidence level d. all of the above e. a and c only

8.35 The probability distribution of an estimator or statistic is a a. random sample b. confidence interval c. null hypothesis d. summary statistic e. sampling distribution


8.36 Analysts for a tire manufacturer estimate from a random sample that mean tread life for its new radial belt tire is between 20,000 and 50,000 miles. Which of the following strategies might be used to obtain a narrower confidence interval?

a. Use a point estimate. b. Collect a larger sample. c. Use a smaller value for . d. Use a larger confidence level. e. All of the above.

8.41 A statement capable of being subjected to empirical evidence is a. a hypothesis b. a tautology c. a theory d. a parameter e. an assumption

8.42 One difference between business statistics and statistics in the sciences is a. business statistics cannot use the scientific method b. sciences do not need to formulate hypotheses c. sciences do not test hypotheses d. human behavior is not as predictable as planets and viruses e. all of the above are differences

8.43 Each of the following is a major source of measurement error in business and economic data except

a. many societies fail to record business and economic data b. governments suppress data to protect confidentiality c. people are reticent to disclose financial information d. businesses are reticent of making information available to rivals e. all of the above are sources of measurement error 8.44 In traditional hypothesis testing, we a. try to reject the null hypothesis b. set up the null hypothesis as a "straw man" c. make the null and alternative hypotheses exhaustive d. make the null and alternative hypotheses mutually exclusive e. all of the above


8.45 What is wrong with the following hypothesis test:

H0: X = 12

HA: X > 12

a. should be stated in terms of 0, not 12 b. should involve population parameters c. does not tell us which is significant d. does not involve a confidence interval e. all of the above 8.46 A type II error is a. rejecting H0 when we shouldn't have b. rejecting HA when we shouldn't have c. not rejecting H0 when we should have d. not rejecting HA when we should have e. the answer depends on the particulars of the problem 8.47 Alpha, , is a. the level of significance b. the probability of a type I error c. the chance we take that our significance judgments are wrong d. the chance we take that we are incorrect when rejecting H0 e. all of the above

8.48 In a two-sided test, each rejection region corresponds to a tail containing probability area equal to

a. 1 - b. 1 - c. / 2 d. / 2 e.

8.49 A formula that may be calculated from sample information and hypothesized values in H0 is called

a. a rejection region b. a decision rule c. a test statistic d. a significance level


e. an hypothesis test

8.50 Which of the following is not a limitation of statistical significance? a. in large samples, significance can be found from minor

Study Guide for ECO 3411

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