VIEWS: 38 PAGES: 18 POSTED ON: 7/18/2012 Public Domain
Review Questions 1. A student wonders if people of similar heights tend to date each other. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man whom each woman dates. Here are the data (heights in inches): Women 64 65 65 66 66 70 Men 68 68 69 70 72 74 Determine whether each of the following statements is true or false. a) If we had measured the heights of the men and women in centimeters (1 inch 2.5 cm), the correlation coefficient would have been 2.5 times larger. b) There is a strong negative association between the heights of men and women because the women are always smaller than the men they date. c) There is a positive association between the heights of men and women. d) Any height above 70 inches must be considered an outlier. Review Questions 2. Determine whether each of the following statements regarding the correlation coefficient is true or false. a) If r is the correlation between X and Y, then –r is the correlation between Y and X. b) If r is the correlation between X and Y, then 2r is the correlation between 2X and Y. Review Questions 3. In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the midterm exam. The equation of the least-squares regression line was y = 10 + 0.9x, where y represents the final exam score and x is the midterm exam score. Suppose Joe scores a 90 on the midterm exam. What would be the predicted value of his score on the final exam? A) 81 B) 89 C) 91 D) Cannot be determined from the information given. We also need to know the correlation. Review Questions 4. In a study of 1991 model cars, a researcher computed the least squares regression line of price (in dollars) on horsepower. He obtained the following equation for this line price = – 6677 + 175 × horsepower. Based on the least-squares regression line, what would we predict the cost of a 1991 model car with horsepower equal to 200 to be? A) $41,677 B) $28,323 C)$35,000 D)$13,354 Review Questions 5. The correlation coefficient between two variables X and Y is r = 0.121. What conclusion can we draw? a) Because the correlation is so low, the relationship between X and Y is not very strong, thus there is no use in studying this relationship. b) Because the correlation is so low, we only know that the linear relationship between X and Y is not very strong, but there may a different relationship between the two variables. We need to first look at a scatterplot. c) The correlation between X and Y is low, but that does not matter. We can still use least-squares regression to calculate an equation of the form = ax + b. d) None of the above. Use the following to answer questions 6-8: A market research company employs a large number of typists to enter data into a computer data base. The time it takes for potential new typists to learn the computer system is known to have a normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes. A candidate is automatically hired if she learns the computer system in less than 100 minutes. A cut-off time is set at the slowest 10% of the learning distribution. Anyone slower than this cut-off time is definitely not hired. 6) What proportion of candidates takes more than two hours to learn the computer system? • A)0.048 B)0.452 C)0.711 D)0.952 7) What proportion of candidates will be automatically hired? • A)0.048 B)0.452 C)0.711 D)0.952 • Answer: • 8) What is the cut-off time the market research company uses? A)1 hour and 7 minutes. B)1 hour and 53 minutes. C)2 hours. D)2 hours and 8 minutes. Determine whether each of the following statements is true or false. 9. The margin of error for a 95% confidence interval for the mean m increases as the sample size increases. 10. The margin of error for a confidence interval for the mean m, based on a specified sample size n, increases as the confidence level decreases. 11. The margin of error for a 95% confidence interval for the mean m decreases as the population standard deviation decreases. 12. The sample size required to obtain a confidence interval of specified margin of error m, increases as the confidence level increases. • Answer: Use the following to answer questions 13 and 14: The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured. The sample mean is 66.2 inches. Suppose that the heights of male high school sophomores follow a normal distribution with standard deviation s = 4.1 inches. 13. What is a 95% confidence interval for m? A) (58.16, 74.24) B)(59.46, 72.94) C) (65.80, 66.60) D)(65.86, 66.54) 14. Suppose the heights of a simple random sample of 100 male sophomores were measured rather than 400. Which of the Following statements is true? A) The margin of error for the 95% confidence interval would increase. B) The margin of error for the 95% confidence interval would decrease. C) The margin of error for the 95% confidence interval would stay the same, because the level of confidence has not changed. D) The standard deviation s would decrease. 15. The scores on the Wechsler Intelligence Scale for Children (WISC) are thought to be normally distributed with standard deviation s = 10. A simple random sample of 25 children is taken, and each is given the WISC. The mean of the 25 scores is = 104.32. Based on these data, what is a 95% confidence interval for m? A) 104.32 ± 0.78 B) 104.32 ± 3.29 C) 104.32 ± 3.92 D) 104.32 ± 19.60 Use the following to answer questions 16 and 17: Battery packs in radio-controlled racing cars need to be able to last pretty long. The distribution of the lifetimes of battery packs made by Lectric Co. is slightly left skewed. Assume that the standard deviation of the lifetime distribution is s = 2.5 hours. A simple random sample of 75 battery packs results in a mean = 29.6 hours. 16. What is a 90% confidence interval for m, the true average lifetime of the battery packs made by Lectric Co.? A) (29.13, 30.07) B)(29.03, 30.17) C)(28.86, 30.34) D) The confidence interval cannot be calculated, because the population distribution is not normal. • • 17. Determine whether each of the following statements is true or false. A) If a 95% confidence interval had been calculated, the margin of error would have been larger. B) If many more samples of 75 battery packs were taken, 90% of the resulting confidence intervals would have a sample mean between 29.13 and 30.07. C) If the sample size had been 150 and not 75, the margin of error would have been larger. 18. Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five students who recently took the exam are 550, 620, 710, 520, and 480.What is a 95% confidence interval for m, the 481.population mean score on the SAT Math test? A) (456.7, 695.3) B) (463.4, 688.6) C) (480.8, 671.2) D) (496.5, 655.5) Use the following to answer questions 21-24: Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. Net weights actually vary slightly from bag to bag. Assume net weights are normally distributed. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses H0: m = 14, Ha: m < 14. To do this, he selects 16 bags of tortilla chips of this brand at random and determines the net weight of each. He finds a sample mean of 13.88 oz. with a standard deviation of s = 0.24 oz. 19. What is the value of the test statistic? • A) t = –0.50 B) t = –2.00 C) t = –8.00 D) t = –8.33 • Answer: 20. Determine which of the following statements regarding the decision the representative would make is true. A) He would not reject H0 at a significance level of 0.05. B) He would reject H0 at a significance level 0.05, but not at 0.025. C) He would reject H0 at a significance level 0.025, but not at 0.01. D) He would reject H0 at a significance level 0.01. • Answer: • Use the following to answer questions 24-26: After once again losing a football game to the college’s arch rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach. • 21. What is a 99% confidence interval for p? • A) 0.64 ± 0.048 B)0.64 ± 0.079 C)0.64 ± 0.094 • D) 0.64 ± 0.124 • Answer: • 22. Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach. To do this they test the hypotheses H0: p = 0.50 versus Ha: p > 0.50. What is the P-value for this hypothesis test? • A) below 0.001 • B) 0.0026 • C) 0.0682 • D) 0.14 • • 23. Suppose the alumni association wished to conduct the test at a 5% significance level. What would their decision be? Based on that decision, what type of mistake could they have made? A) Accept H0, Type I error B) Accept H0, Type II error C) Reject H0, Type I error D)Reject H0, Type II error Answer Key 1. A) False, B) False, C) True, D) False 2. A) False, B) False 3. C 4. C 5. B 6. A 7. C 8. B 9. False 10.False 11) True, 12) True • 13. C • 14. A • 15. C • 16. A • 17. A) True, B) False, C) False, D) True • 18. B • 19. B 20. B 21. D 22. B • 23. C