BUS 713 Sampling Distributions and Estimation; Hypothesis Testing | Complete Solution

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

2.    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. 63.14 to 85.26
B. 64.92 to 83.48
C. 13.64 to 134.76
D. 68.72 to 79.68

3.    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.    In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.
C.    A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true.
D.    The rejection region is always given in units of standard deviations from the mean.

4.    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. 0.9975
B. 0.995
C. 0.050
D. 0.005

5.    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 falls in the acceptance region.
 
B.    No, because the test statistic is –1.85 and falls in the rejection region.
C.    Yes, because the test statistic is greater than –1.645.
D.    Yes, because the sample mean of 9.25 is below 9.5.

6.    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 researcher should use the z-test because the population is assumed to be normally distributed.
B.    The t-test should be used because α and μ are unknown.
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.

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. 0.5062
C. 0.6535
D. 0.3465

8.    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. 0.4963
D. 0.0074

9.    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 achieve a more accurate result than can be achieved by surveying the entire population
D.    To verify that the population is approximately normally distributed

10.    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
 
11.    Which of the following statements about p-value testing is   true?
A.    The p-value is the lowest significance level at which you should reject H0.
B.    P-value testing applies only to one-tail tests.
C.    The p represents sample proportion.
D.    P-value testing uses a predetermined level of significance.

12.    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.    Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.
C.    Use t when the sample size is small, and the resulting confidence interval will be narrower.
D.    The value of z relates to a normal distribution, while the value of t relates to a Poisson distribution.

13.    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. 200
B. 500
C. 400
D. 600

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

15.    What is the primary reason for applying a finite population correction   coefficient?
A.    If you don't apply the correction coefficient, your confidence intervals will be too broad, and thus less useful in decision making.
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.    When the sample is a very small portion of the population, the correction coefficient is required.
D.    If you don't apply the correction coefficient, your confidence intervals will be too narrow, and thus overconfident.

16.    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.

17.    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 H0. At the 0.01 level, the sample data suggest that the average price- earnings ratio for the stocks is less than 20.
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.    If z > 2.33, reject H0.
D.    If t > 2.68 or if t < –2.68, reject H0.

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

19.    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

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. 6.69
B. 3.32
C. 0.95
D. –3.32