Sampling Distributions and Estimation; Hypothesis Testing

1. A random sample of 10 employees is selected from a large firm. For the 10 employees, the number of days each was absent during the past month was found to be 0, 2, 4, 2, 5, 1, 7, 3, 2, and 4. Of the following values, which would you use as the point estimate for the average number of days absent for all the firm’s employees?
A. 30
B. 2.5
C. 4
D. 3
2. A federal auditor for nationally chartered banks, from a random sample of 100 accounts, found that the average demand deposit balance at the First National Bank of Arkansas was $549.82. If the auditor needed a point estimate for the population mean for all accounts at this bank, what should he use?
A. The average of $549.82 for this sample
B. There’s no acceptable value available.
C. The auditor should survey the total of all accounts and determine the mean.
D. The average of $54.98 for this sample
3. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the test statistic?
A. –2.68
B. –2.64
C. 2.64
D. 2.68
4. Nondirectional assertions lead only to _______-tail tests.
A. right
B. one
C. left
D. two
5. In a criminal trial, a Type II error is made when a/an
A. innocent person is convicted.
B. innocent person is acquitted.
C. guilty defendant is convicted.
D. guilty defendant is acquitted.
6. Determine which of the following four population size and sample size combinations would not require the use of the finite population correction factor in calculating the standard error.
A. N = 2500; n = 75
B. N = 1500; n = 300
C. N = 15,000; n = 1,000
D. N = 150; n = 25
7. Determine the power for the following test of hypothesis.
H0 : μ = 950 vs. H1 : μ ≠ 950, given that μ = 1,000, α = 0.10, σ = 200, and n = 25.
A. 0.4938
B. 0.3465
C. 0.5062
D. 0.6535
8. The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven’t really been stolen. What null and alternative hypotheses would be appropriate in evaluating this statement made by the commissioner?
A. H0: p ≤ 0.10 and H1: p > 0.10
B. H0: p = 0.10 and H1: p ≠ 0.10
C. H0: p > 0.10 and H1: p ≤ 0.10
D. H0: p ≥ 0.10 and H1: p < 0.10
9. What sample size is required from a very large population to estimate a population proportion within 0.05 with 95% confidence? Don’t assume any particular value for p.
A. 767
B. 271
C. 385
D. 38
10. In sampling without replacement from a population of 900, it’s found that the standard error of the mean is only two-thirds as large as it would have been if the population were infinite in size. What is the approximate sample size?
A. 400
B. 500
C. 200
D. 600
11. In a simple random sample from a population of several hundred that’s approximately normally distributed, the following data values were collected.
68, 79, 70, 98, 74, 79, 50, 102, 92, 96
Based on this information, the confidence level would be 90% that the population mean is somewhere between
A. 73.36 and 88.24.
B. 69.15 and 92.45.
C. 65.33 and 95.33.
D. 71.36 and 90.24.
12. What is the purpose of sampling?
A. To create a point estimator of the population mean or proportion
B. To estimate a target parameter of the population
C. To verify that the population is approximately normally distributed
D. To achieve a more accurate result than can be achieved by surveying the entire population
13. When the confidence coefficient is large, which of the following is true?
A. It’s more likely that the test will lead you to reject the null hypothesis.
B. The confidence interval is narrow.
C. Its value is close to 1.0, but not larger than 1.0.
D. Its value is 1.0 or larger.
14. If the level of significance (α) is 0.005 in a two-tail test, how large is the nonrejection region under the curve of the t distribution?
A. 0.995
B. 0.005
C. 0.9975
D. 0.050
15. A portfolio manager was analyzing the price-earnings ratio for this year’s performance. His boss said that the average price-earnings ratio was 20 for the many stocks that his firm had traded, but the portfolio manager felt that the figure was too high. He randomly selected a sample of 50 price-earnings ratios and found a mean of 18.17 and a standard deviation of 4.60. Assume that the population is normally distributed, and test at the 0.01 level of significance. Which of the following is the correct decision rule for
the manager to use in this situation?
A. If z > 2.33, reject H0.
B. Because 2.81 is greater than 2.33, reject H0. At the 0.01 level, the sample data suggest that the average price-earnings ratio
for the stocks is less than 20.
C. Because –2.81 falls in the rejection region, reject H0. At the 0.01 level, the sample data suggest that the average price earnings
ratio for the stocks is less than 20.
D. If t > 2.68 or if t < –2.68, reject H0.
16. The power of a test is the probability of making a/an _______ decision when the null hypothesis is_______.
A. incorrect, false
B. correct, false
C. incorrect, true
D. correct, true
17. H0 is p = 0.45 and H1 is p ≠ 0.45. What type of test will be performed?
A. Two-tail testing of a proportion
B. One-tail testing of a mean
C. Two-tail testing of a mean
D. One-tail testing of a proportion
18. Which of the following statements about p-value testing is true?
A. P-value testing applies only to one-tail tests.
B. The p-value is the lowest significance level at which you should reject H0.
C. P-value testing uses a predetermined level of significance.
D. The p represents sample proportion.
19. Which of the following statements about hypothesis testing is false?
A. The test will never confirm the null hypothesis, only fail to reject the null hypothesis.
B. A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true.
C. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.
D. The rejection region is always given in units of standard deviations from the mean.
20. What is the rejection region for a two-tailed test when α = 0.05?
A. |z | > 1.645
B. z > 2.575
C. |z | > 1.96
D. |z | > 2.575