Sampling Distributions and Estimation; Hypothesis Testing

Student ID: 21458913

Exam: 250713RR - 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 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 $54.98 for this sample

B. The average of $549.82 for this sample

C. There's no acceptable value available.

D. The auditor should survey the total of all accounts and determine the mean.

2. 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 α and μ are unknown. 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 the sample size is small.

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

3. 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. One-tail testing of a proportion

D. Two-tail testing of a proportion

4. 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

5. 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. H

0 : p ≥ 0.10 and H

1 : p < 0.10

B. H0: p ≤ 0.10 and H1: p > 0.10

C. H 0

: p > 0.10 and H 1

: p ≤ 0.10

D. H0: p = 0.10 and H1: p ≠ 0.10

6. For 1996, the U.S. Department of Agriculture estimated that American consumers would have eaten, on average, 2.6 pounds of cottage cheese throughout the course of that year. Based on a longitudinal study of 98 randomly selected people conducted during 1996, the National Center for Cottage Cheese Studies found an average cottage cheese consumption of 2.75 pounds and a standard deviation of s = 14 ounces. Given this information, which of the following statements would be correct concerning a two-tail test at the 0.05 level of significance? A. We can conclude that the average cottage cheese consumption in America is actually 2.75 pounds per person per year.

B. We can conclude that the average cottage cheese consumption in America isn't 2.6 pounds per person per year.

C. We can conclude that the average cottage cheese consumption in America is at least 0.705 pound more or less than 2.75 pounds per person per year.

D. We can conclude that we can't reject the claim that the average cottage cheese consumption in America is 2.6 pounds per person per year.

7. 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. 271

B. 767

C. 385

D. 38

8. In a criminal trial, a Type II error is made when a/an A. guilty defendant is acquitted.

B. innocent person is acquitted.

C. innocent person is convicted.

D. guilty defendant is convicted.

9. 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. 200

C. 600

D. 500

10. The power of a test is the probability of making a/an _______ decision when the null hypothesis is _______. A. correct, true

B. correct, false

C. incorrect, false

D. incorrect, true

11. Nondirectional assertions lead only to _______-tail tests. A. right

B. one

C. two

D. left

12. 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. 2.5

B. 3

C. 4

D. 30

13. Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume that s = $0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within $0.25 of the true mean ticket prices? A. 4

B. 16

C. 8

D. 15

14. 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. Because –2.81 falls in the rejection region, reject H

0 . At the 0.01 level, the sample data suggest that the average price-

earnings ratio for the stocks is less than 20.

B. If z > 2.33, reject H0.

C. If t > 2.68 or if t < –2.68, reject H 0 .

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.

15. Determine the power for the following test of hypothesis. H

0 : μ = 950 vs. H

1 : μ ≠ 950, given that μ = 1,000, α = 0.10, σ = 200, and n = 25.

A. 0.5062

B. 0.6535

C. 0.4938

D. 0.3465

16. In the statement of a null hypothesis, you would likely find which of the following terms? A. <

B. =

C. >

D. ≠

17. 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.

18. To schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient? A. 18.3, 95%

B. 20.3, 95%

C. 20.3, 0.95

D. 18.3, 0.95

19. 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. one, mean

C. one, proportion

D. two, proportion

20. What is the primary reason for applying a finite population correction coefficient? A. When the sample is a very small portion of the population, the correction coefficient is required.

B. 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.

C. If you don't apply the correction coefficient, your confidence intervals will be too narrow, and thus overconfident.

D. If you don't apply the correction coefficient, your confidence intervals will be too broad, and thus less useful in decision making.

End of exam