Please select the correct answer and state briefly why:
1. A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs. and 24 lbs. respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will be less than 94 lbs. is:
A. 34.13%
B. 84.13%
C. 15.87%
D. 56.36%
E. 16.87%
2. 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. The historical records of the company show that over the past 8 years 13 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that more than 40 accounts will be classified as delinquent?
A. 42.07%
B. 92.07%
C. 7.93%
D. 40.15%
E. 90.15%
3. If we have a sample size of 100 and the estimate of the population proportion is 0.10, the mean of the sampling distribution of the sample proportion is:
A. 0.0009
B. 0.10
C. 0.03
D. 0.90
E. 0.09
4. The width of a confidence interval will be:
A. Narrower for 95% confidence than 99% confidence
B. Wider for a sample size of 100 than for a sample size of 50
C. Wider for 90% confidence than 95% confidence
D. Wider when the sample standard deviation (s) is small than when s is large
5. When the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be __________ when p(1-p) is smaller than when p(1-p) is larger.
A. Narrower
B. Wider
C. Neither A nor B, they will be the same
D. Cannot tell from the information given
6. A confidence interval increases in width as
A. The level of confidence increases
B. n decreases
C. s increases
D. All of the above
E. None of the above
7. 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. 2.769 to 3.231
D. 2.412 to 3.588
E. 2.814 to 3.186
8. 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
9. 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. 1549
C. 897
D. 632
E. 1267
10. A company is interested in estimating the mean number of days of sick leave taken by its employees. The firm’s statistician randomly selects 100 personnel files and notes the number of sick days taken by each employee. The sample mean is 12.2 days and the sample standard deviation is 10 days. How many personnel files would the director have to select in order to estimate ï to within 2 days with a 99% confidence interval?
A. 2
B. 135
C. 136
D. 165
E. 166
11. If a null hypothesis is rejected at a significance level of .10, it will ______ be rejected at a significance level of .05
A. Always
B. Sometimes
C. Never
12. If a null hypothesis is not rejected at a significance level of .05, it will ______ be rejected at a significance level of .01
A. Always
B. Sometimes
C. Never
13. When carrying out a large sample test of H0: ?=10 vs. Ha: ? ï?¹ 10 by using a p-value, we reject H0 at level of significance ? when the p-value is:
A. Greater than ?/2
B. Greater than ?
C. Less than ?
D. Less than ?/2
E. Less than Z?
14. If you live in California, the decision to buy earthquake insurance is an important one. A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance. Calculate the appropriate test statistic to test the hypotheses that at least 40% buy the insurance. (rounded)
A. 0.20
B. 0.39
C. -0.13
D. -0.20
E. -0.39
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