CHAPTER 11Strategies for Analyzing Quantitative Data

Q1._________are characteristics of samples, whereas __________ are characteristics of populations.Ans. Statistics, parametersQ2.In a normal distribution, what percentage of scores falls between one standard deviation below the mean and one standard deviation above the mean?68.2 %Q3. In a normal distribution, what percentage of scores falls between two standard deviation below the mean and two standard deviation above the mean?95.4 %Q4.In a normal distribution, what percentage of scores falls between one standard deviation below the mean and two standard deviation above the mean?81.8 %Q5.In a normal distribution, what percentage of scores higher than one standard deviationabove the mean?15.9 %

Q6.In a normal distribution, what percentage of scores lower than between two standard deviation above the mean?84.1 %

Q7.Here is a set of scores: 15, 13, 17, 13, 16, 12, 15, 13. The mean of this set of scores is ______.Ans. (15+13+17+13+16+12+15+13) / 8 Mean = 14.25Q8. Here is a set of scores: 15, 13, 17, 13, 16, 12, 15, 13. The median of this set of scores is ______.Ans. 1213131315151617Median = 13 + 15 / 2 = 14Q9.Here is a set of scores: 15, 13, 17, 13, 16, 12, 15, 13. The mode of this set of scores is ______.Ans. 13Q10. Here is a set of scores in a sample: 19, 13, 17, 13, 18, 12, 15, 11, 8.The Variance of this set of scores is __________.Show your work?Ans. Mean = (19+13+17+13+18+12+15+11+8) / 9 = 14XM(X - M)2

19525

13-11

1739

13-11

18416

12-24

1511

11-39

8-636

102

Variance = (X - M)2 / n -1 102 / 9 1 = 12.75Q11.Here is a set of scores for a sample of9 observation19, 13, 17, 13, 18, 12, 15, 11, 8.The standard deviation of this set of scores is ______.Show your workAns. Mean = (19+13+17+13+18+12+15+11+8) / 9 = 14XM(X - M)2

19525

13-11

1739

13-11

18416

12-24

1511

11-39

8-636

102

Variance = (X - M)2 / n -1 102 / 9 1 = 12.75Standard Deviation = Square root of variance Square root of 12.75 = 3.57

Q12.The measure(s) of central tendency that is/are appropriate for use with nominal data is/are: a. the median only. b. the mode only. c. the median and the mean. d. the median and the mode.Ans. B. The mode onlyQ13.When summarizing ordinal data, the ______ is the most useful measure of central tendency.a. the median only. b. the mode only.c. the median and the mean. d. the median and the mode.Ans. D. The median and the modeQ14. An exam was given to two sections of the same course. In Section 1, the exam mean was 51 and the standard deviation was 7. In Section 2, the exam mean was 51 and the standard deviation was 13. Which of the following conclusions is accurate?a. Section 1 did better on the exam than Section 2.b. Section 1 scores were more variable than Section 2.c. Section 1 scores were less variable than Section 2.d. Section 1 did less well on the exam than Section 2.Ans. C.Section 1 scores were less variable than Section 2

Q15. An exam was given to two sections of the same course. In Section 1, the exam mean was 69 and the standard deviation was 17. In Section 2, the exam mean was 51 and the standard deviation was 17. Which of the following conclusions is accurate?a. Section 1 did better on the exam than Section 2.b. Section 1 scores were more variable than Section 2.c. Section 1 scores were less variable than Section 2.d. Section 1 did less well on the exam than Section 2.Ans. A. Section 1 did better on the exam than Section 2.

Q16. Thez-score, or standard score, allows the research to determine:a. how far a target individuals score is from the group mean.b. what percentage of individuals in the sample scored above the target individual.c. the mean for the population based on the mean for the sample.d. what percentage of individuals in the sample scored below the target individual.Ans. A. How far a target individuals score is from the group mean.

Q17. The percentile rank allows the researcher to determine:a. how far a target individuals score is from the group mean.b. what percentage of individuals in the sample scored above the target individual.c. the mean for the population based on the mean for the sample.d. what percentage of individuals in the sample scored below the target individual.Ans. D. What percentage of individuals in the sample scored below the target individual.Q18.Seamus has determined that there is a 95% chance that the number of people visiting the Blarney Stone in the month of June will be between 1,760 and 2,025. This is a/an ______ estimate.a. point b. intervalAns. B. Interval

Q19.In a simple random sample of 100 high school students, the sample mean of the SAT scoreswas 1450, and the sample standard deviation was 180.a. Find a point estimate of the population mean of all the high school students SAT scores from which the sample was drawn.b. Find a 95.4% confidence interval for the population mean of all the high school students SAT scores from which the sample was drawn.Ans. A. Point of estimateis the mean of the sample i.e. 1450B. Total number of high school students n = 100Standard Deviation = 18095.4% confidence interval for population mean = 1450+/- (2*180) / (100) ^1/2 = 1450 +/- (360) / 10 = 1450 +/- 36Therefore the confidence interval for the population mean of all high school students SAT scores form which the sample was drawn (1486, 1414).

Q20.In a simple random sample of 121 high school students, the sample mean of the SAT scoreswas 1450, and the sample standard deviation was 190. Test the null hypothesis that the population of all the high school students SAT scores from which the sample was drawn is 1400 vs the research hypothesis is different from 1400. (use a significance level of 5%)Show the null and hypothesis , the test statistic value Z, test and make a conclusion.Ans. n = 121Sample mean=1450Standard deviation=190Null hypothesis H0 = 1400Research hypothesis, Ha1400Z= (1450-1400)/ (190/121) = 50/190*11 = 2.89Since 2.89 is greater than 2 (as significance level of 5%)We reject the null hypothesis and support research hypothesis.Q21.In a simple random sample of 100 high school students , the sample mean of the SAT scores was 1430, and the sample standard deviation was 200. Test the null hypothesis that the population of all the high school students SAT scores from which the sample was drawn is 1400 vs the research hypothesis is different from 1400. (use a significance level of 5%)Show the null and hypothesis, the test statistic value Z, test and make a conclusion.Ans. Given n = 100Sample mean = 1430Standard deviation = 200Null hypothesis H0 = 1400Research hypothesis, Ha 1400Z= (1430-1400)/ (200/100) = 30/200*10 = 1.5Since 1.5 lies between -Z and Zi.e. 2 < 1.5 < 2 (Z=2 as significance level of 5%), we do not reject the null hypothesis.Q22.Statistical hypothesis testing involves testing the___________ hypothesis and then make a decision about the ___________ hypothesis.Ans. Null, Research.

Q23.On the basis of statistical findings, Ron determines that the differences between males and females on a test of spatial reasoning are not due merely to chance. If, in fact, there are no gender differences in the population, Ron will have made a:a. Type I error. b. Type II error.Ans. A. Type I error

Q24.On the basis of statistical findings, Becky determines that the difference between males and females on a test of abstract mathematical reasoning is merely due to chance. If, in fact, there are gender differences in the population, Becky will have made a:a. Type I error. b. Type II error.Ans. B. Type II errorSUMITH R BATTULARESEARCH METHODS