1.For a two-tailed hypothesis test with a sample size of 20 and a .05 level of significance, the critical values of the test statistic t are
| a. -2.086 and 2.086. |
| b. -1.729 and 1.729. |
| c. -2.093 and 2.093. |
| d. -1.725 and 1.725 |
2. Which of the following statements is true with respect to hypothesis testing?
| a. All hypothesis tests are two-sided. |
| b. The p-value approach and critical value approach will always provide the same hypothesis-testing conclusion. |
| c. The level of significance must be known before computing a p-value for a hypothesis test. |
| d. All of these choices are true. |
3. For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,
| a. will have no effect on the area corresponding to the critical value. |
| b. will result in the area corresponding to the critical value being smaller. |
| c. Not enough information is given to answer this question. |
| d. will result in the area corresponding to the critical value being larger. |
4. Which of the following represents a Type I error for the null and alternative hypotheses H0: μ ≤ $3,200 and Ha: μ > $3,200, where μ is the average amount of money in a savings account for a person aged 30 to 40?
| a. A Type I error would occur if we reject H0 and conclude that the average age is less than 30 when in fact the average age is greater than 40. |
| b. A Type I error would occur if we reject H0 and conclude that the average amount is greater than $3,200 when in fact the average amount is $3,200 or less. |
| c. A Type I error would occur if we fail to reject H0 and conclude that the average amount is $3,200 or less when in fact the average amount is greater than $3,200. |
| d. A Type I error would occur if we fail to reject H0 and conclude that the average amount is less than or equal to $3,200 when in fact the average amount is $3,200 or less. |
5. The p-value is a probability that measures the support (or lack of support) for
| a. the alternative hypothesis. |
| b. the null hypothesis. |
| c. either the null or the alternative hypothesis. |
| d. neither the null nor the alternative hypothesis. |
6. The probability of making a Type I error is denoted by
| a. 1 – α. |
| b. β. |
| c. α. |
| d. 1 – β. |
7. Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (lower tail) with 22 degrees of freedom at α = .05, the value of t =
| a. 1.383. |
| b. -1.717. |
| c. -1.721. |
| d. -1.383. |
8. The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are
| a. H0: μ = 40.1 Ha: μ ≠ 40.1. |
| b. H0: μ < 40.1 Ha: μ ≥ 40.1. |
| c. H0: μ ≥ 40.1 Ha: μ < 40.1. |
| d. H0: μ > 40.1 Ha: μ ≤ 40.1. |
9. In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to
| a. 2α. |
| b. α. |
| c. 1 – α/2. |
| d. α/2 |
10. Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (upper tail) at α = .0630, z =
| a. 1.645. |
| b. 1.53. |
| c. 1.50. |
| d. 1.96. |
11. A machine produces parts on an assembly line for an automotive manufacturer. If a part is defective, it must be scrapped. Every hour, the manager takes a random sample of 15 parts to test whether the process is “out of control” (i.e., to test whether the average proportion of defective parts exceeds 10%). Which of the following is a Type I error for this situation?
| a. A Type I error for this situation would be to conclude that an out of control process is in control. |
| b. A Type I error for this situation would be to incorrectly conclude that the process is out of control. |
| c. A Type I error for this situation would be to correctly conclude that the process is in control. |
| d. A Type I error for this situation would be to conclude that an out of control process is out of control |
12. In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to
| a. α. |
| b. α/2. |
| c. 2α. |
| d. 1 – α/2 |
13. In a two-tailed hypothesis test situation, the test statistic is determined to be t = -2.692. The sample size has been 45. The p-value for this test is
| a. -.01. |
| b. +.01. |
| c. -.005. |
| d. +.005. |
14. A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The correct null hypothesis for this problem is
| a. μ = 8000. |
| b. μ ≤ 8300. |
| c. μ > 8300. |
| d. μ ≤ 8000. |
15. standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. The test statistic is
| a. 1.96. |
| b. .05. |
| c. 2.00. |
| d. 1.65 |
16. A sample of 1400 items had 280 defective items. For the following hypothesis test,
H0: p ≤ .20
Ha: p > .20
the test statistic is
| a. .14. |
| b. .20. |
| c. .28. |
| d. zero. |
17. Batteries produced by a manufacturing company have had a life expectancy of 135 hours. Because of an improved production process, the company believes that there has been an increase in the life expectancy of its batteries. A sample of 42 batteries showed an average life of 140 hours. From past information, the standard deviation of the population is known to be 24 hours. Test to determine whether there has been an increase in the life expectancy of batteries. What is the test statistic, and what conclusion can be made at the .10 level of significance?
| a. z = 1.35; Reject the null hypothesis |
| b. z = .208; Do not reject the null hypothesis |
| c. z = .088; Do not reject the null hypothesis |
| d. z = 2.33; Reject the null hypothesis |
18. For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,
| a. will result in the area corresponding to the critical value being larger. |
| b. will result in the area corresponding to the critical value being smaller. |
| c. will have no effect on the area corresponding to the critical value. |
| d. Not enough information is given to answer this question |
19. The standard error of x̄1 – x̄2 is the
| a. pooled estimator of x̄1 – x̄2. |
| b. variance of the sampling distribution of x̄1 – x̄2. |
| c. standard deviation of the sampling distribution of x̄1 – x̄2. |
| d. margin of error of x̄1 – x̄2. |
20. Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on
| a. pooled samples. |
| b. research samples. |
| c. conditional samples. |
| d. independent samples. |
21. A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.
| Today | Five Years Ago | |
| x̄ | 82 | 88 |
| σ2 | 112.5 | 54 |
| n | 45 | 36 |
The standard error of x̄1 – x̄2 is
| a. 12.9. |
| b. 4. |
| c. 9.3. |
| d. 2. |
22. The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store’s credit card versus those customers using a national major credit card. You are given the following information.
| Store’s Card | Major Credit Card | |
| Sample size | 64 | 49 |
| Sample mean | $140 | $125 |
| Population standard deviation | $10 | $8 |
At 95% confidence, the margin of error is
| a. 1.694. |
| b. 1.96. |
| c. 15. |
| d. 3.32. |
23. The following information was obtained from independent random samples. Suppose we are interested in testing H0: µ1 – µ2 = 15 and Ha: µ1 – µ2 ≠ 15.
What is the test statistic used in the hypothesis test for the difference between the two population means?
| a. –5.49 |
| b. 14.07 |
| c. –1.37 |
| d. .829 |
24. The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.
| Sample 1 | Sample 2 | |
| Sample Mean | 45 | 42 |
| Sample Variance | 85 | 90 |
| Sample Size | 10 | 12 |
The degrees of freedom for the t distribution are
| a. 22. |
| b. 20. |
| c. 21. |
| d. 24. |
25. When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as
| a. pooled samples. |
| b. independent samples. |
| c. corresponding samples. |
| d. matched samples. |
26. A researcher is interested in determining whether the mean of group 1 is 10 units larger than the mean of group 2. Which of the following represents the alternative hypothesis for testing the researcher’s theory?
| a. Ha: µ1 – µ2 > 10 |
| b. Ha:µ1 – µ2 = 0 |
| c. Ha: µ 1 – µ2 ≤ 10 |
| d. Ha: µ1 = µ2 |
27. The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed.
| Individual | Method 1 | Method 2 |
| 1 | 7 | 5 |
| 2 | 5 | 9 |
| 3 | 6 | 8 |
| 4 | 7 | 7 |
| 5 | 5 | 6 |
If the null hypothesis H0: μd = 0 is tested at the 5% level,
| a. the null hypothesis should not be rejected. |
| b. the null hypothesis should be revised. |
| c. the null hypothesis should be rejected. |
| d. the alternative hypothesis should be revised. |
28. Salary information regarding male and female employees of a large company is shown below.
| Male | Female | |
| Sample Size | 64 | 36 |
| Sample Mean Salary (in $1000) | 44 | 41 |
| Population Variance (σ2) | 128 | 72 |
The standard error of the difference between the two sample means is
| a. 2.0. |
| b. 4. |
| c. 7.46. |
| d. 4.24. |
29. The following information was obtained from matched samples:
If the null hypothesis tested is H0: µd = 0, what is the test statistic for the difference between the two population means?
| a. –.24 |
| b. –.50 |
| c. .51 |
| d. –.48 |
30. Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.
| Driver | Manufacturer A | Manufacturer B |
| 1 | 32 | 28 |
| 2 | 27 | 22 |
| 3 | 26 | 27 |
| 4 | 26 | 24 |
| 5 | 25 | 24 |
| 6 | 29 | 25 |
| 7 | 31 | 28 |
| 8 | 25 | 27 |
The test statistic is
| a. 1.906. |
| b. 1.616. |
| c. 2.256. |
| d. 2.096. |
31. Two independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the
| a. t distribution with 60 degrees of freedom. |
| b. t distribution with 58 degrees of freedom. |
| c. t distribution with 59 degrees of freedom. |
| d. t distribution with 61 degrees of freedom |
32. Two independent types of a product were produced. The dollar amount of sales for each type over a one-month period was recorded. Assume the sales values are normally distributed. The results are given in the table below.
What are the p-value and conclusion for the hypothesis test of H0: µ1 – µ2 = 0 vs. Ha: µ1 – µ2 < 0 using α = 0.05?
| a. p = 1.326; Do not reject H0. |
| b. p = .0924; Do not reject H0. |
| c. p = .0924; Reject H0. |
| d. p = 0; Reject H0. |
33. An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.
| Under Age of 18 | Over Age of 18 |
| n1 = 500 | n2 = 600 |
| Number of accidents = 180 | Number of accidents = 150 |
We are interested in determining if the accident proportions differ between the two age groups. The p-value is
| a. less than .001. |
| b. .3. |
| c. more than .10. |
| d. .0228. |
34. Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.
| Driver | Manufacturer A | Manufacturer B |
| 1 | 32 | 28 |
| 2 | 27 | 22 |
| 3 | 26 | 27 |
| 4 | 26 | 24 |
| 5 | 25 | 24 |
| 6 | 29 | 25 |
| 7 | 31 | 28 |
| 8 | 25 | 27 |
The mean of the differences is
| a. .5. |
| b. 2.0. |
| c. 1.5. |
| d. 2.5. |
35. Production output (i.e., number of parts) for a random sample of days from two different plants is shown below.
What is the estimate of the standard deviation for the difference between the two means?
| a. 75 |
| b. 5.12 |
| c. 14.66 |
| d. 130.34 |
36. A school administrator is interested in determining whether the proportion of students in the elementary school who are girls (pE) is significantly more than the proportion of students in the high school who are girls (pH). Which set of hypotheses would be most appropriate for answering the administrator’s question?
| a. H0 : pE – pH ≤ 0 Ha : pE – pH > 0 |
| b. H0 : pE – pH = 0 Ha : pE – pH ≠ 0 |
| c. H0: pE – pH < 0 Ha: pE – pH ≥ 0 |
| d. H0 : pE – pH ≥ 0 Ha : pE – pH < 0 |
37. The results of a recent poll on the preference of shoppers regarding two products are shown below.
| Product | Shoppers Surveyed | Shoppers Favoring This Product |
| A | 800 | 560 |
| B | 900 | 612 |
The point estimate for the difference between the two population proportions in favor of this product is
| a. .44. |
| b. .07. |
| c. .68. |
| d. .02. |
38. An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.
| Under Age of 18 | Over Age of 18 |
| n1 = 500 | n2 = 600 |
| Number of accidents = 180 | Number of accidents = 150 |
We are interested in determining if the accident proportions differ between the two age groups. The p-value is
| a. .3. |
| b. less than .001. |
| c. more than .10. |
| d. .0228. |
39. Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.
| a. single, independent |
| b. independent, pooled |
| c. matched, independent |
| d. matched, pooled |
40. The sampling distribution of p̄1 – p̄2 is approximated by a normal distribution if _____ are all greater than or equal to 5.
| a. n1p2, n1(1 – p2), n2p1, n2(1 – p1) |
| b. n1p1, p1(1 – n1), n2p2, p2(1 – n2) |
| c. n1p2, p2(1 – n2), n2p1, p1(1 – n1) |
| d. n1p1, n1(1 – p1), n2p2, n2(1 – p2) |
41. Which of the following is not true with respect to tests for the difference between two means when the population standard deviations are known?
| a. The samples must come from normally distributed populations or the sample sizes must be large enough to apply the central limit theorem. |
b. The margin of error for a confidence interval estimate is  . |
| c. The samples must be randomly and independently selected. |
| d. The test statistic for a hypothesis test has a t distribution. |
42. The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.
| Sample 1 | Sample 2 | |
| Sample Mean | 45 | 42 |
| Sample Variance | 85 | 90 |
| Sample Size | 10 | 12 |
The 95% confidence interval for the difference between the two population means is (use rounded standard error)
| a. -4.86 to 10.86. |
| b. -5.344 to 11.344. |
| c. -2.65 to 8.65. |
| d. -5 to 3. |
43. Salary information regarding male and female employees of a large company is shown below.
| Male | Female | |
| Sample Size | 64 | 36 |
| Sample Mean Salary (in $1000) | 44 | 41 |
| Population Variance (σ2) | 128 | 72 |
The standard error of the difference between the two sample means is
| a. 7.46. |
| b. 4.24. |
| c. 4. |
| d. 2.0. |
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