Example

In a certain city, there are about one million eligible voters. A simple random sample of size 100 was chosen to study the relationship between gender and participation in the last election. The results were as follows:

Men Women Total

Voted 27 35 62

Not voted 14 24 38

Total 41 59 100

Men Women Total

Voted (62*41)/100 =25.42

(62*59)/100 =36.58

62

Not voted (41*38)/100 =15.58

(38*59)/100 =22.42

38

41 59 100

Men-

observe Men expected

Women observe

Women expected

Voted 27

25.42 35 36.58

Not voted

14 15.58 24 22.42

Total

For p-value of the test,useTI-83/84 chi sqare dist.

If the p value is greater than 0.05, we will fail to reject the null hypothesis and say there is not sufficient evidence to support alternate hypotheses.

Review test 3

9 question 2 free response(take the practice test 3)

1) What will reduce the width of a confidence interval?

2) A simple random sample of 49 8th graders at a large suburban middle school indicated that 84% of them are involved with some type of after school activity. Find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity.

3) Television viewers often express doubts about the validity of certain commercials. In an attempt to answer their critics, a large advertiser wants

to estimate the true proportion of consumers who believe what is shown in commercials. Preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. What is the minimum number of consumers that should be sampled by the advertiser to be 99% confident that their estimate will fall within 2% of the true population proportion?

4) The gas mileage for a certain model of car is known to have a standard

deviation of 6 mi/gallon. A simple random sample of 49 cars of this model is chosen and found to have a mean gas mileage of 28.4 mi/gallon. Construct a 97% confidence interval for the mean gas mileage for this car model. (TI84_Stat ZInterval number 7)

5) A 97% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit. A preliminary sample standard deviation is 1.7. The smallest sample size n that provides the desired accuracy is Calculate 97% CI TI-84: =2.17 In_norm(.97+(1-.97)/2)=Inv_norm(.985)=2.17

6) An SRS of 28 students at UH gave an average height of 5.9 feet and a

standard deviation of .1 feet. Construct a 90% confidence interval for the mean height of students at UH.

TI-84:TI interval

7) An auditor for a hardware store chain wished to compare the efficiency of two different auditing techniques. To do this he selected a sample of nine store accounts and applied auditing techniques A and B to each of the nine accounts selected. The number of errors found in each of techniques A and B is listed in the table below:

Select a 99% confidence interval for the true mean difference in the two techniques.

TI-84:TI interval

Errors in A Errors in B 27 13 30 19 28 21 30 19 34 36 32 27 31 31 22 23 27 32

8) True or false

a) In a hypothesis test, if the computed P-value is less than 0.001, there is very strong evidence to fail to reject the null hypothesis. Ans : reject the null hypothesis.

b) In a hypothesis test, if the computed P-value is greater than a specified level of significance, then we Ans : fail to reject the null hypothesis.

9) It is believed that the average amount of money spent per U.S. household per week on food is about $99, with standard deviation $10. A random sample of 25 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average. State the null and alternative hypotheses for this test, the test statistic and determine if the results significant at the 5% level.

TI -84 Z-Test

10) Let x represent the hemoglobin count (HC) in grams per 100 milliliters of whole blood. The distribution for HC is approximately normal with μ = 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood samples in the last year. The HC data sent to her doctor is listed below. We would like to know if the data indicates this patient has significantly high HC compared to the population.

State the null and alternate hypothesis, give the p-value and state your conclusion

based on a 5% significance level.

TI- 84 use Ttest

I get

t= 1.428

P=.09

Sample mean =15.4

Sample sd= 3.098

N=10

11) An experimenter flips a coin 100 times and gets 44 heads. Test the claim that the coin is fair against the two-sided claim that it is not fair at the level α=.01.

12) In a experiment on relaxation techniques, subject's brain signals were measured before and after the relaxation exercises with the following results:

Person 1 2 3 4 5 Before 31 37 66 52 28 After 26 34 58 51 26

Assuming the population is normally distributed, is there sufficient evidence to suggest that the relaxation exercise slowed the brain waves? (Use α=0.05)

13) Identify the most appropriate test to use for the following situation: A national computer retailer believes that the average sales are greater for salespersons with a college degree. A random sample of 14 salespersons with a degree had an average weekly sale of $3542 last year, while 17 salespersons without a college degree averaged $3301 in weekly sales. The standard deviations were $468 and $642 respectively. Is there evidence to support the retailer’s belief?

14) Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results:

We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic? (assume the population data is normally distributed)

15) It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group wil be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode? Select the [Rejection Region, Decision to Reject (RH0) or Failure to Reject (FRH0)].

Invnorm(.1/2)=1.64485

16) A private and a public university are located in the same city. For the private university, 1046 alumni were surveyed and 643 said that they attended at least one class reunion. For the public university, 804 out of 1315 sampled alumni claimed they have attended at least one class reunion. Is the difference in the sample proportions statistically significant? (Use α=0.05) TI-84 2-Prop Ztest

p1 is not equal p2

z=0.164

p=.869

p1=.614

p2=.611

17) Mars Inc. claims that they produce M&Ms with the following distributions:

Brown 20% Red 25% Yellow 25% Orange 5% Green 15% Blue 10%

A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:

Brown 25 Red 23 Yellow 21 Orange 13 Green 15 Blue 14

Using the χ2 goodness of fit test (α = 0.05) to determine if the proportion of M&Ms is what is claimed. Select the [test statistic, p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].

1) You will need to do free response like one or more of the following: A confidence interval about a mean or a proportion. A hypothesis test on a single mean, dependent means or single proportion. A hypothesis test on two independent means or proportions. For your hypothesis tests, be able to state the null and alternate hypothesis, sketch the rejection region, find the critical value, find the p-value and state your conclusion (in complete sentences using terms from the problem).

Final Exam outline: 18 m/c (no f/r) 1-13 are 5 pts each and 14-18 are 7 pts each Topics:

• Probability distributions • Normal distributions • Conditional probabilities • Choosing correct hypothesis test • Mean and variance (or standard deviation) of probability distributions • Mena and variance (or standard deviation) of linear combinations of

distributions (E[aX+b], Var[aX+b]) • Find c such that P(Z < c) = some value • Standard error of sample proportion • Confidence intervals • Probability rules (several questions on this) • Binomial distribution probabilities • Geometric distribution probabilities • LSRL, r, r2, residuals • Hypothesis tests