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BA 275 Review Problems - Week 4 (10/16/06 - 10/20/06) CD Lessons: 35, 40 - 47 Textbook: pp. 362 - 374 1. Suppose we want a 90% confidence interval for the average amount spent on books by Freshman in their first year at a major university. The interval is to have a margin of error of $2, and the amount spent has a normal distribution, with a standard deviation σ = $30. The number of observations required is closest to A) 25. B) 30. C) 609. D) 865. 2. You measure the weights of a random sample of 400 male workers in the automotive industry. The sample mean is x = 176.2 lbs. Suppose that the weights of male workers in the automotive industry follow a normal distribution with unknown mean µ and standard deviation σ = 11.1 lbs. I compute a 95% confidence interval for µ. Suppose I measure the weights of a random sample of 100 workers rather than 400. Which of the following statements is true? A) The margin of error for my 95% confidence interval would be larger than yours. B) The margin of error for my 95% confidence interval would be smaller than yours. C) The margin of error for my 95% confidence interval would be the same as yours, because the level of confidence has not changed. D) σ would decrease. 3. A 95% confidence interval for the mean µ of a population is computed from a random sample and found to be 9 ± 3. We may conclude A) there is a 95% probability that µ is between 6 and 12. B) there is a 95% probability that the true mean is 9 and there is a 95% chance that the true margin of error is 3. C) if we took many, many additional random samples and from each computed a 95% confidence interval for µ, approximately 95% of these intervals would contain µ. D) all of the above. Page 1 4. Researchers are studying sales of department stores in two locations. The researchers are going to compute independent 90% confidence intervals for the mean sales of department stores at each location. The probability that at least one of the intervals will cover the true mean yields at that location is A) 0.81. B) 0.19. C) 0.99. D) 0.95. 5. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a normal distribution with mean µ and standard deviation σ = 25. A simple random sample of 25 college students is taken and each is given the SSHA. The mean of the 25 scores is x = 114.32. Suppose a histogram of the 25 SSHA scores is given below. 5 4 3 2 1 75 95 115 135 155 175 195 SSHA A) B) C) D) Based on this histogram, we would conclude the 95% confidence interval computed from these data is very reliable. the 95% confidence interval computed from these data is not very reliable. the 95% confidence interval computed from these data is actually a 99% confidence interval. the 95% confidence interval computed from these data is actually a 90% confidence interval. Page 2 6. Twenty-five credit card holders are selected at random. For each, their current credit card balance is recorded. The average for these 25 people is x = $600. Assume that the current balance of all credit card holders follows a normal distribution with unknown mean µ, and that a 90% confidence interval for µ is found to be $600 ± $32.90. What can we deduce about the standard deviation σ of current credit card balances? A) σ is about $100. B) σ will be larger than if we used 100 credit card holders. C) σ is $32.90. D) If we repeatedly took samples of 25 credit card holders many, many additional times and from each sample computed a 90% confidence interval, in approximately 90% of these σ would be within $32.90 of the mean. 7. To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean x of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean µ and standard deviation σ = 0.01 g. How large should n be so that a 95% confidence interval for µ has a margin of error of ± 0.0001? A) 100 B) 196 C) 10000 D) 38416 8. Twenty-five credit card holders are selected at random. For each, their current credit card balance is recorded. The average for these 25 people is x = $600. Assume that the current balance of all credit card holders follows a normal distribution with unknown mean µ and standard deviation σ = $100. A 90% confidence interval for µ is A) $600 ± $20. B) $600 ± $32.90. C) $600 ± $39.20. D) $600 ± $329.00. 9. In a large city, the percent of total spending that households devote to housing is normally distributed with mean µ and standard deviation σ = 9%. If I want the margin of error for a 99% confidence interval to be ±1%, I should select a simple random sample of size A) 9. B) 23. C) 312. D) 538. 10. The distribution of a critical dimension of the crankshaft produced by a manufacturing plant for a certain type of automobile engine is normal, with mean µ and standard deviation σ = 0.02 mm. Suppose I select a simple random sample of four of the crankshafts produced by the plant and measure this critical dimension. The results of these four measurements are 200.01 A) B) C) D) 199.98 200.00 200.01. Based on these data, a 90% confidence interval for µ is 200.00 ± 0.00082. 200.00 ± 0.00115. 200.00 ± 0.00165. 200.00 ± 0.00196. 11. A study was conducted to compare the weights of sedentary workers with the weights of workers in physically demanding jobs. As part of the study, the weights of male accountants between the ages of 35 and 50 were recorded. Suppose a 99% confidence interval for the mean weight of accountants in pounds is (172.3, 176.5). If we had measured the weights of each of the accountants in kilograms (2.2 pounds = 1 kilogram), then the confidence interval for the mean weight of such accountants in kilograms would have been A) (174.5, 176.7). B) (78.32, 80.23). C) (379.06, 388.3). D) (170.1, 174.3). 12. Suppose that the population of the scores of all high school seniors who took the Math SAT test this year follows a normal distribution with mean µ and standard deviation σ = 100. You read a report that says, “on the basis of a simple random sample of 100 high school seniors who took the Math SAT test this year, a confidence interval for m is 512.00 ± 25.76.” The confidence level for this interval is A) 90%. B) 95%. C) 99%. D) over 99.9%. 13. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a normal distribution with mean µ and standard deviation σ = 25. A simple random sample of 25 college students is taken and each is given the SSHA. The mean of the 25 scores is x = 114.32. Based on these data, a 95% confidence interval for µ is A) 114.32 ± 1.96. B) 114.32 ± 9.80. C) 114.32 ± 19.60. D) 114.32 ± 49.00. Page 4 14. The records of the 100 postal employees at a postal station in a large city showed that the average time these employees had worked for the postal service was x = 8 years. Assume that we know that the standard deviation of the population of times U.S. postal service employees have spent with the postal service is approximately normal, with standard deviation σ = 5 years. A 95% confidence interval for the mean time µ the population of U.S. postal service employees has spent with the postal service based on these data is A) 8 ± 0.82. B) 8 ± 0.98. C) 8 ± 9.80. D) not trustworthy. Page 5 Answer Key 1. C Topic: 2. A Topic: 3. C Topic: 4. C Topic: 5. B Topic: 6. A Topic: 7. D Topic: 8. B Topic: 9. D Topic: 10. C Topic: 11. B Topic: 12. C Topic: 13. B Topic: 14. D Topic: 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence 6.1 Estimating With Confidence Page 6