Case BA 302 ( BA 302) Chapter 07answers

The t distribution always has n degrees of freedom. Answer: False Difficulty: Easy 2. Assuming the same level of significance α, as the sample size increases, the value of tα/2 approaches the value of zα/2. Answer: True Difficulty: Medium 3. When constructing a confidence interval for a sample proportion, the t distribution is appropriate if the sample size is small. Answer: False Difficulty: Medium 4. When the population is normally distributed and the population standard deviation  is unknown, then for any sample size n, the sampling distribution of is based on the z distribution. Answer: False Difficulty: Medium (REF) 5. When the sample size and sample standard deviation remain the same, a 99% confidence interval for a population mean,  will be narrower than the 95% confidence interval for . Answer: False Difficulty: Medium (REF) 6. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be narrower than a confidence interval for a population mean based on a sample of n = 50. Answer: True Difficulty: Medium 7. When the level of confidence and the sample size remain the same, a confidence interval for a population mean  will be wider, when the sample standard deviation s is small than when s is large. Answer: False Difficulty: Medium 8. When the level of confidence and sample proportion remain the same, a confidence interval for a population proportion p based on a sample of n = 100 will be wider than a confidence interval for p based on a sample of n = 400. Answer: True Difficulty: Medium 9. When the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be narrower when is larger than when is smaller. Answer: False Difficulty: Medium (REF) 10. When solving for the sample size needed to compute a 95% confidence interval for a population proportion “p”, having a given error bound “B”, we choose a value of that makes as small as reasonably possible. Answer: False Difficulty: Medium (REF) 11. When determining the sample size n, if the value found for n is 79.2, we would choose to sample 79 observations. Answer: False Difficulty: Medium (REF) Multiple Choice 12. The t distribution approaches the _______________ as the sample size ___________. A) Binomial, increases B) Binomial, decreases C) Z, decreases D) Z, increases Answer: D Difficulty: Medium (REF) 13. The width of a confidence interval will be: A) Narrower for 99% confidence than 95% confidence. B) Wider for a sample size of 100 than for a sample size of 50. C) Narrower for 90% confidence than 95% confidence. D) Wider when the sample standard deviation (s) is small than when s is large. Answer: C Difficulty: Medium 14. As standard deviation increases, samples size _____________ to achieve a specified level of confidence. A) Increases B) Decreases C) Remains the same Answer: A Difficulty: Medium 15. When determining the sample size, if the value found is not an integer initially, the next highest integer value will ____________ be chosen. A) Always B) Sometimes C) Never Answer: A Difficulty: Medium 16. When constructing a confidence interval for a population mean, if a population is normally distributed and a small sample is taken, then the distribution of is based on _____ distribution. A) z B) t C) Neither D) Both A and B Answer: B Difficulty: Medium 17. A confidence interval increases in width as A) The level of confidence increases B) n decreases C) s increases D) All of the above Answer: D Difficulty: Medium (REF) 18. The width of a confidence interval will be: A) Narrower for 98% confidence than for 90% confidence. B) Wider for a sample size of 64 than for a sample size of 36. C) Wider for a 99% confidence than for 95% confidence D) Narrower for sample size of 25 than for a sample size of 36. E) None of the above Answer: C Difficulty: Medium 19. A Research and Development Laboratory researcher for a paint company is measuring the level a certain chemical contained in a certain type of paint. If the paint contains too much of this chemical, the quality of the paint will be compromised. On the average, each can of paint contains 10% of the chemical, How many cans of paint should the sample contain if the researcher wants to be 98% certain of being within 1% of the true proportion of this chemical? A) 4887 B) 1107 C) 26 D) 645 Answer: A Difficulty: Medium (AS) 20. Which of the following is an advantage of confidence interval estimate over a point estimate for a population parameter? A) Interval estimates are more precise than point estimates. B) Interval estimates are less accurate than point estimates. C) Interval estimates are both more accurate and more precise than point estimates. D) Interval estimates take into account the fact that the statistic being used to estimate the population parameter is a random variable. Answer: D Difficulty: Medium 21. When the sample size and sample standard deviation remain the same, a 99% confidence interval for a population mean,  will be _________________ the 95% confidence interval for . A) Wider than B) Narrower than C) Equal to Answer: A Difficulty: Medium (REF) 22. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be ______________ a confidence interval for a population mean based on a sample of n = 50. A) Wider than B) Narrower than C) Equal to Answer: B Difficulty: Medium 23. When the level of confidence and the sample size remain the same, a confidence interval for a population mean  will be ________________, when the sample standard deviation s is small than when s is large. A) Wider B) Narrower C) Neither A nor B, they will be the same Answer: B Difficulty: Medium 24. When the sample size and the sample proportion remain the same, a 90% confidence interval for a population proportion p will be ______________ the 99% confidence interval for p. A) Wider than B) Narrower than C) Equal to Answer: B Difficulty: Medium 25. When the level of confidence and sample proportion remain the same, a confidence interval for a population proportion p based on a sample of n = 100 will be ______________ a confidence interval for p based on a sample of n = 400. A) Wider than B) Narrower than C) Equal to Answer: A Difficulty: Medium 26. When the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be ______________ when is larger than when is smaller. A) Wider B) Narrower C) Neither A nor B, they will be the same Answer: A Difficulty: Medium 27. When the population is normally distributed, population standard deviation  is unknown, and the sample size is n = 15; the confidence interval for the population mean  is based on the: A) z (normal) distribution B) t distribution C) Binomial distribution D) Poisson Distribution E) None of the above Answer: B Difficulty: Medium 28. When solving for the sample size needed to compute a 95% confidence interval for a population proportion “p”, having a given error bound “B”, we choose a value of that makes: A) as small as reasonably possible B) as large as reasonably possible C) as close to .5 as reasonably possible D) as close to .25 as reasonably possible E) Both B and D are correct Answer: E Difficulty: Medium (REF) 29. When a confidence interval for a population proportion is constructed for a sample size n = 30 and the value of = .4, the interval is based on the: A) z distribution B) t distribution C) exponential distribution D) Poisson distribution E) None of the above Answer: A Difficulty: Medium 30. There is little difference between the values of tα/2 and zα/2 when the sample: A) size is small B) size is large C) mean is small D) mean is large E) standard deviation is small Answer: B Difficulty: Medium 31. Assuming the same level of significance , as the sample size increases, the value of t/2 _____ approaches the value of . A) Always B) Sometimes C) Never Answer: A Difficulty: Medium 32. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a variance of .09. What is the 90% confidence interval for the true mean length of the bolt? A) 2.8355 to 3.1645 B) 2.5065 to 3.4935 C) 2.4420 to 3.5580 D) 2.8140 to 3.8160 E) 2.9442 to 3.0558 Answer: D Difficulty: Hard 33. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 95% confidence interval for the true mean length of the bolt? A) 2.804 to 3.196 B) 2.308 to 3.692 C) 2.770 to 3.231 D) 2.412 to 3.588 E) 2.814 to 3.186 Answer: C Difficulty: Hard 34. In a manufacturing process a random sample of 36 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 99% confidence interval for the true mean length of the bolt? A) 2.902 to 3.098 B) 2.884 to 3.117 C) 2.871 to 3.129 D) 2.228 to 3.772 E) 2.902 to 3.098 Answer: C Difficulty: Medium 35. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). For this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. What is the 95% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company? A) .1608 to .2392 B) .1992 to .2008 C) .1671 to .2329 D) .1485 to .2515 E) .1714 to .2286 Answer: A Difficulty: Hard 36. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are current (between 0 and 60 days after billing). The historical records show that over the past 8 years 70 percent of the accounts have been current. Determine the sample size needed in order to be 99% confident that the sample proportion of the current customer accounts is within .03 of the true proportion of all current accounts for this company. A) 1842 B) 1548 C) 897 D) 632 E) 1267 Answer: B Difficulty: Hard 37. In a manufacturing process, we are interested in measuring the average length of a certain type of bolt. Past data indicates that the standard deviation is .25 inches. How many bolts should be sampled in order to make us 95% confident that the sample mean bolt length is within .02 inches of the true mean bolt length? A) 25 B) 49 C) 423 D) 601 E) 1225 Answer: D Difficulty: Hard 38. In a manufacturing process, we are interested in measuring the average length of a certain type of bolt. Based on a preliminary sample of 9 bolts, the sample standard deviation is .3 inches. How many bolts should be sampled in order to make us 95% confident that the sample mean bolt length is within .02 inches of the true mean bolt length? A) 864.36 B) 80 C) 1470 D) 3989 E) 1197 Answer: E Difficulty: Hard Fill-in-the-Blank 39. In the construction of a confidence interval, as the confidence level required in estimating the mean increases, the width of the confidence interval ______________. Answer: increases Difficulty: Medium