Stats exam

Questions 1 to 20: Select the best answer to each question.

1. What is the rejection region for a two-tailed test when α = 0.05?
A. |z | > 1.645
B. |z | > 2.575
C. z > 2.575
D. |z | > 1.96

2. 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 p-value you would report for this test?
A. 0.0037
B. 0.0041
C. 0.0074
D. 0.4963

3. 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. 500
B. 400
C. 200
D. 600

4. Nondirectional assertions lead only to _______-tail tests.
A. left
B. one
C. two
D. right

5. 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 = 150; n = 25
C. N = 1500; n = 300
D. N = 15,000; n = 1,000

6. A woman and her son are debating about the average length of a preacher's sermons on Sunday
morning. Despite the mother's arguments, the son thinks that the sermons are more than twenty minutes.
For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a
standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05
level of significance, he wishes to determine whether he is correct in thinking that the average length of
sermons is more than 20 minutes. What is the test statistic?
A. 0.95
B. 3.32
C. –3.32
D. 6.69

7. H0 is p = 0.45 and H1 is p ≠ 0.45. What type of test will be performed?
A. Two-tail testing of a mean
B. One-tail testing of a mean
C. Two-tail testing of a proportion
D. One-tail testing of a proportion

8. In a criminal trial, a Type II error is made when a/an
A. guilty defendant is convicted.
B. guilty defendant is acquitted.
C. innocent person is acquitted.
D. innocent person is convicted.

9. Which of the following statements about p-value testing is true?
A. The p represents sample proportion.
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. P-value testing applies only to one-tail tests.

10. 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. 0.3465
B. 0.5062
C. 0.6535
D. 0.4938

11. 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. 0.005
B. 0.995
C. 0.9975
D. 0.050

12. 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 auditor should survey the total of all accounts and determine the mean.
B. The average of $54.98 for this sample
C. There's no acceptable value available.
D. The average of $549.82 for this sample

13. A researcher wants to carry out a hypothesis test involving the mean for a sample of n = 20. While the
true value of the population standard deviation is unknown, the researcher is reasonably sure that the
population is normally distributed. Given this information, which of the following statements would be
correct?
A. The t-test should be used because the sample size is small.
B. The researcher should use the z-test because the population is assumed to be normally distributed.
C. The t-test should be used because α and μ are unknown.
D. The researcher should use the z-test because the sample size is less than 30.

14. What is the purpose of sampling?
A. To achieve a more accurate result than can be achieved by surveying the entire population
B. To verify that the population is approximately normally distributed
C. To estimate a target parameter of the population
D. To create a point estimator of the population mean or proportion

15. 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. 3
B. 4
C. 30
D. 2.5

16. 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. 69.15 and 92.45.
B. 71.36 and 90.24.
C. 73.36 and 88.24.
D. 65.33 and 95.33.

17. Which of the following statements about hypothesis testing is false?
A. The rejection region is always given in units of standard deviations from the mean.
B. A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true.
C. The test will never confirm the null hypothesis, only fail to reject the null hypothesis.
D. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.

18. A human resources manager wants to determine a confidence interval estimate for the mean test score
for the next office-skills test to be given to a group of job applicants. In the past, the test scores have been
normally distributed with a mean of 74.2 and a standard deviation of 30.9. Determine a 95% confidence
interval estimate if there are 30 applicants in the group.
A. 13.64 to 134.76
B. 64.92 to 83.48
C. 68.72 to 79.68
D. 63.14 to 85.26

19. A mortgage broker is offering home mortgages at a rate of 9.5%, but the broker is fearful that this value
is higher than many others are charging. A sample of 40 mortgages filed in the county courthouse shows an
average of 9.25% with a standard deviation of 8.61%. Does this sample indicate a smaller average? Use α
= 0.05 and assume a normally distributed population.
A. No, because the test statistic is –1.85 and falls in the rejection region.
B. Yes, because the sample mean of 9.25 is below 9.5.
C. Yes, because the test statistic is greater than –1.645.
D. No, because the test statistic falls in the acceptance region.

20. What is the primary reason for applying a finite population correction coefficient?
A. If you don't apply the correction coefficient, you won't have values to plug in for all the variables in the confidence interval
formula.
B. When the sample is a very small portion of the population, the correction coefficient is required.
C. If you don't apply the correction coefficient, your confidence intervals will be too broad, and thus less useful in decision
making.
D. If you don't apply the correction coefficient, your confidence intervals will be too narrow, and thus overconfident.