# Sampling distributions and estimation; hypothesis testing

Sampling Distributions and Estimation; Hypothesis Testing

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Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page

break, so be sure that you have seen the entire question and all the answers before choosing an answer.

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. 3

B. 2.5

C. 30

D. 4

2. In a criminal trial, a Type II error is made when a/an

A. guilty defendant is acquitted.

B. innocent person is convicted.

C. guilty defendant is convicted.

D. innocent person is acquitted.

3. What is the purpose of sampling?

A. To create a point estimator of the population mean or proportion

B. To achieve a more accurate result than can be achieved by surveying the entire population

C. To verify that the population is approximately normally distributed

D. To estimate a target parameter of the population

4. What is the rejection region for a two-tailed test when α = 0.05?

A. |z | > 1.96

B. z > 2.575

C. |z | > 2.575

D. |z | > 1.645

5. Which of the following statements about p-value testing is true?

A. P-value testing uses a predetermined level of significance.

B. P-value testing applies only to one-tail tests.

C. The p represents sample proportion.

D. The p-value is the lowest significance level at which you should reject H0.

6. Which of the following statements correctly compares the t-statistic to the z-score when creating a

confidence interval?

A. You can use t all the time, but for n ≥ 30 there is no need, because the results are almost identical if you use t or z.

B. The value of z relates to a normal distribution, while the value of t relates to a Poisson distribution.

C. Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.

D. Use t when the sample size is small, and the resulting confidence interval will be narrower.

7. If a teacher wants to test her belief that more than five students in college classes typically receive A as a

grade, she’ll perform _______-tail testing of a _______.

A. two, mean

B. two, proportion

C. one, mean

D. one, proportion

8. 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. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.

D. The test will never confirm the null hypothesis, only fail to reject the null hypothesis.

9. 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. 2.64

B. 2.68

C. –2.64

D. –2.68

10. 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. Yes, because the test statistic is greater than –1.645.

B. No, because the test statistic is –1.85 and falls in the rejection region.

C. No, because the test statistic falls in the acceptance region.

D. Yes, because the sample mean of 9.25 is below 9.5.

11. 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 t-test should be used because α and μ are unknown.

C. The researcher should use the z-test because the sample size is less than 30.

D. The researcher should use the z-test because the population is assumed to be normally distributed.

12. The power of a test is the probability of making a/an _______ decision when the null hypothesis is

_______.

A. correct, true

B. incorrect, true

C. correct, false

D. incorrect, false

13. 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 = 150; n = 25

B. N = 1500; n = 300

C. N = 15,000; n = 1,000

D. N = 2500; n = 75

14. When the confidence coefficient is large, which of the following is true?

A. Its value is 1.0 or larger.

B. It’s more likely that the test will lead you to reject the null hypothesis.

C. The confidence interval is narrow.

D. Its value is close to 1.0, but not larger than 1.0.

15. 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. 600

C. 400

D. 200

16. 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. 385

B. 38

C. 271

D. 767

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. Two-tail testing of a mean

C. One-tail testing of a mean

End of exam

D. One-tail testing of a proportion

18. 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 t > 2.68 or if t < –2.68, reject H0.

B. If z > 2.33, reject H0.

C. Because –2.81 falls in the rejection region, reject H0. At the 0.01 level, the sample data suggest that the average priceearnings

ratio for the stocks is less than 20.

D. 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.

19. Nondirectional assertions lead only to _______-tail tests.

A. right

B. one

C. left

D. two

20. 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. 6.69

C. 3.32

D. –3.32

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