| n = 30 | H0: σ2 = 500 |
| s2 = 625 | Ha: σ2 ≠ 500 |
The test statistic equals
| a. 24.00. |
| b. 36.25. |
| c. 23.20. |
| d. 37.50 |
2. The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The test statistic is
| a. 30. |
| b. 1.2. |
| c. 500. |
| d. 31.2. |
3. Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B.
| Sample A | Sample B | |
| n | 11 | 10 |
| s2 | 12.1 | 5 |
The test statistic for this problem equals
| a. 2. |
| b. 2.42. |
| c. 1.1. |
| d. .4132. |
4. The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is .05 or less. The null hypothesis in a test to confirm the claim would be written as
| a. H0: σ2 > .05. |
| b. H0: σ2 ≥ .05. |
| c. H0: σ2 < .05. |
| d. H0: σ2 ≤ .05 |
5. Consider the following hypothesis problem.
| n = 23 | s2 = 60 | H0: σ2 ≤ 66 |
| Ha: σ2 > 66 |
If the test is to be performed at the .05 level of significance, the null hypothesis
| a. should not be tested. |
| b. should be rejected. |
| c. should be revised. |
| d. should not be rejected. |
6. Consider the scenario where
The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the table is(are) _____.
| a. 5.629 |
| b. 5.629 and 26.119 |
| c. 6.262 and 27.488 |
| d. 27.488 |
7. A sample of 61 observations yielded a sample standard deviation of 6. If we want to test H0: σ2 = 40, the test statistic is
| a. 9. |
| b. 54.90. |
| c. 54. |
| d. 9.15. |
8. Given the sample information below, what test statistic should be used to determine whether the standard deviations are equal for two populations, prior to performing a hypothesis test for the equality of the population means?
| a. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19 |
| b. F = 0.40, with degrees of freedom = 19 |
| c. t = 18.75, with degrees of freedom = 19 |
| d. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29 |
9. Consider the following sample information from Population A and Population B.
| Sample A | Sample B | |
| n | 24 | 16 |
| s2 | 32 | 38 |
We want to test the hypothesis that the population variances are equal. The null hypothesis is to be tested at the 10% level of significance. The critical value from the F distribution table is
| a. 2.24. |
| b. 2.11. |
| c. 2.29. |
| d. 2.13. |
10. The random variable for a chi-square distribution may assume
| a. any value between -1 to 1. |
| b. any value greater than zero. |
| c. any value between -∞ to +∞. |
| d. any negative value. |
11. Consider the following hypothesis problem.
| n = 14 | H0: σ2 ≤ 410 |
| s = 20 | Ha: σ2 > 410 |
The test statistic equals
| a. .63. |
| b. 13.33. |
| c. 13.68. |
| d. 12.68. |
12. The χ2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 20 is _____.
| a. 10.851 |
| b. 10.117 |
| c. 30.144 |
| d. 31.410 |
13. The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The p-value for this test is
| a. zero. |
| b. .05. |
| c. less than .10. |
| d. greater than .10. |
14. The sampling distribution used when making inferences about a single population’s variance is
| a. a t distribution. |
| b. an F distribution. |
| c. a chi-square distribution. |
| d. a normal distribution. |
15. The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the
| a. chi-square distribution. |
| b. normal distribution. |
| c. t distribution. |
| d. F distribution. |
16. Consider the following hypothesis problem.
| n = 23 | s2 = 60 | H0: σ2 ≤ 66 |
| Ha: σ2 > 66 |
If the test is to be performed at the .05 level of significance, the null hypothesis
| a. should not be tested. |
| b. should be rejected. |
| c. should not be rejected. |
| d. should be revised. |
17. We are interested in testing whether the variance of a population is significantly more than 625. The null hypothesis for this test is
| a. H0: σ2 > 625. |
| b. H0: σ2 ≤ 625. |
| c. H0: σ2 ≥ 625. |
| d. H0: σ2 ≤ 25. |
18. A sample of 20 bottles of soda yielded a standard deviation of .25 ounce. A 95% confidence interval estimate of the variance for the population is _____.
| a. .0361 to .1333 |
| b. –.6378 to .6378 |
| c. .0394 to .1174 |
| d. .0023 to .0083 |
19. To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let the
| a. sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic. |
| b. smaller sample variance be the numerator of the test statistic. |
| c. larger sample variance be the numerator of the test statistic. |
| d. sample variance from the population with the larger hypothesized variance be the numerator of the test statistic. |
20. The value of F.01 with 9 numerator and 20 denominator degrees of freedom is
| a. 2.39. |
| b. 2.91. |
| c. 2.94. |
| d. 3.46. |
21. The chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of 25 is
| a. 36.415. |
| b. 37.652. |
| c. 33.196. |
| d. 39.364. |
22. Which of the following rejection rules is proper?
| a. Reject H0 if p-value ≥ α/2. |
| b. Reject H0 if F ≥ Fα. |
| c. Reject H0 if F ≤ Fα/2. |
| d. Reject H0 if p-value ≤ Fα. |
23. The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is
| a. 8.576 to 39.794. |
| b. 9.46 to 34.09. |
| c. 2.144 to 9.948. |
| d. 2.93 to 6.31. |
24. χ2.975 = 8.231 indicates that
| a. 97.5% of the chi-square values are less than 8.231. |
| b. 5% of the chi-square values are equal to 8.231. |
| c. 2.5% of the chi-square values are greater than 8.231. |
| d. 97.5% of the chi-square values are greater than 8.231. |
25. Consider the following hypothesis problem.
| n = 30 | H0: σ2 = 500 |
| s2 = 625 | Ha: σ2 ≠ 500 |
The test statistic equals
| a. 36.25. |
| b. 37.50. |
| c. 23.20. |
| d. 24.00. |
26. Consider the following hypothesis problem.
| n = 30 | H0: σ2 = 500 |
| s2 = 625 | Ha: σ2 ≠ 500 |
At the 5% level of significance, the null hypothesis
| a. should be revised. |
| b. should not be tested. |
| c. should be rejected. |
| d. should not be rejected. |
27. The value of F.05 with 8 numerator and 19 denominator degrees of freedom is
| a. 2.48. |
| b. 3.63. |
| c. 2.96. |
| d. 2.58. |
28. The symbol used for the variance of the population is
| a. σ2. |
| b. s2. |
| c. s. |
| d. σ. |
29. The sampling distribution of the quantity (n – 1)s2/σ2 is the
| a. normal distribution. |
| b. chi-square distribution. |
| c. F distribution. |
| d. t distribution. |
30. Which of the following is not a property of a chi-square distribution?
| a. χ2 is skewed to the right. |
| b. The number of degrees of freedom defines the shape of the distribution of χ2. |
| c. χ2 can have both positive and negative values. |
| d. All of these choices are properties of the χ2 distribution. |
31. The χ2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 20 is _____.
| a. 10.117 |
| b. 10.851 |
| c. 31.410 |
| d. 30.144 |
32. Which of the following rejection rules is proper?
| a. Reject H0 if p-value ≥ α/2. |
| b. Reject H0 if p-value ≤ Fα. |
| c. Reject H0 if F ≤ Fα/2. |
| d. Reject H0 if F ≥ Fα. |
33. Consider the following hypothesis problem.
| n = 23 | s2 = 60 | H0: σ2 ≤ 66 |
| Ha: σ2 > 66 |
If the test is to be performed at the 5% level, the critical value(s) from the chi-square distribution table is(are)
| a. 12.338 and 33.924. |
| b. 12.338. |
| c. 33.924. |
| d. 10.982 and 36.781. |
34. A manufacturer of carpentry screws claims that its production machine is very accurate and that the standard deviation of the length of all screws produced is .08 mm or less. A sample of 30 screws showed a standard deviation of .10. The test statistic to test the manufacturer’s claim is _____.
| a. 18.56 |
| b. 19.2 |
| c. 45.31 |
| d. 23.2 |
35. The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The test statistic is
| a. 1.2. |
| b. 30. |
| c. 500. |
| d. 31.2. |
36. You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.
| 2 | 3 | 5 | 5 | 7 | 8 | 8 | 9 | 9 | 10 |
| 11 | 11 | 12 | 12 | 12 | 12 | 13 | 13 | 13 | 14 |
| 15 | 15 | 15 | 16 | 16 | 17 | 17 | 18 | 18 | 19 |
The number of intervals or categories used to test the hypothesis for this problem is
| a. 10. |
| b. 4. |
| c. 6. |
| d. 5. |
37. A study was conducted to examine whether the proportion of females was the same for five groups (Groups A, B, C, D, and E). How many degrees of freedom would the χ2 test statistic have when testing the hypothesis that the proportions in each group are all equal?
| a. 0.20 |
| b. 4 |
| c. 5 |
| d. 1 |
38. When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
| Do you support capital punishment? | Number of individuals |
| Yes | 40 |
| No | 60 |
| No Opinion | 50 |
We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the
| a. distribution is uniform. |
| b. distribution might have been normal. |
| c. null hypothesis cannot be rejected. |
| d. Marascuilo procedure is more applicable. |
39. The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is
| a. A chi-square distribution is not used. |
| b. k – 1. |
| c. number of rows minus 1 times number of columns minus 1. |
| d. n – 1. |
40. A population where each of its element is assigned to one and only one of several classes or categories is a
| a. Poisson population. |
| b. multinomial population. |
| c. binomial population. |
| d. normal population. |
41. The table below gives beverage preferences for random samples of teens and adults.
| Teens | Adults | Total | |
| Coffee | 50 | 200 | 250 |
| Tea | 100 | 150 | 250 |
| Soft Drink | 200 | 200 | 400 |
| Other | 50 | 50 | 100 |
| 400 | 600 | 1000 |
We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is
| a. 200. |
| b. .25. |
| c. 150. |
| d. .33. |
42. The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
| Political Party | Support |
| Democrats | 100 |
| Republicans | 120 |
| Independents | 80 |
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is
| a. .333. |
| b. .50. |
| c. 50. |
| d. 100. |
43. Marascuilo procedure is used to test for a significant difference between pairs of population
| a. proportions. |
| b. variances. |
| c. means. |
| d. standard deviations. |
44. Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year’s student body showed the following number of students in each classification.
| Freshmen | 83 |
| Sophomores | 68 |
| Juniors | 85 |
| Seniors | 64 |
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. At a .05 level of significance, the null hypothesis
| a. cannot be tested. |
| b. should not be rejected. |
| c. was designed wrong. |
| d. should be rejected. |
45. Two hundred randomly selected people were asked to state their primary source for news about current events: (1) Television, (2) Radio, (3) Internet, or (4) Other. We wish to determine whether the percent distribution of responses is 10%, 30%, 50%, and 10% for news sources 1 through 4, respectively. What is the null hypothesis?
| a. H0: p = .50 |
| b. H0: the proportions are not all equal. |
| c. H0: p1= .10, p2 = .30, p3 = .50, p4 = .10 |
| d. H0: p1 = .25, p2 = .25, p3 = .25, p4 = .25 |
46. The test for goodness of fit
| a. is always an upper tail test. |
| b. is always a lower tail test. |
| c. can be a lower or an upper tail test. |
| d. is always a two-tailed test. |
47. The table below gives beverage preferences for random samples of teens and adults.
| Teens | Adults | Total | |
| Coffee | 50 | 200 | 250 |
| Tea | 100 | 150 | 250 |
| Soft Drink | 200 | 200 | 400 |
| Other | 50 | 50 | 100 |
| 400 | 600 | 1000 |
We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The test statistic for this test of independence is
| a. 62.5. |
| b. 0. |
| c. 82.5. |
| d. 8.4. |
48. In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The expected frequency for the Business College is
| a. 90. |
| b. .35. |
| c. 105. |
| d. .3. |
49. An important application of the chi-square distribution is
| a. testing for goodness of fit. |
| b. testing for the independence of two categorical variables. |
| c. making inferences about a single population variance. |
| d. All of these alternatives are correct. |
50. A population where each of its element is assigned to one and only one of several classes or categories is a
| a. multinomial population. |
| b. Poisson population. |
| c. normal population. |
| d. binomial population. |
51. When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
| Do you support capital punishment? | Number of individuals |
| Yes | 40 |
| No | 60 |
| No Opinion | 50 |
We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the
| a. distribution is uniform. |
| b. null hypothesis cannot be rejected. |
| c. Marascuilo procedure is more applicable. |
| d. distribution might have been normal. |
52. In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a
| a. z test for proportions. |
| b. test for independence. |
| c. multinomial population. |
| d. Marascuilo procedure |
53. Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year’s student body showed the following number of students in each classification.
| Freshmen | 83 |
| Sophomores | 68 |
| Juniors | 85 |
| Seniors | 64 |
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The expected frequency of seniors is
| a. 68. |
| b. 60. |
| c. 64. |
| d. 20% |
54. The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:
| Number of Cars Arriving in a 10-Minute Interval | Frequency |
| 0 | 3 |
| 1 | 10 |
| 2 | 15 |
| 3 | 23 |
| 4 | 30 |
| 5 | 24 |
| 6 | 20 |
| 7 | 13 |
| 8 | 8 |
| 9 or more | 4 |
| 150 |
The calculated value for the test statistic equals
| a. 1.72. |
| b. .18. |
| c. 3.11. |
| d. 2.89. |
55.
Which of the following Chi-Square tests can be used to determine if a data set follows a Normal distribution?
| a. Chi Square Test of Association |
| b. Chi-Square Test of Homogeneity |
| c. Chi-Square Goodness of Fit |
| d. Chi-Square Test of Equality of Three or More Population Proportions |
56. When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
| Do you support capital punishment? | Number of individuals |
| Yes | 40 |
| No | 60 |
| No Opinion | 50 |
We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the
| a. Marascuilo procedure is more applicable. |
| b. distribution might have been normal. |
| c. distribution is uniform. |
| d. null hypothesis cannot be rejected. |
57. The table below gives beverage preferences for random samples of teens and adults.
| Teens | Adults | Total | |
| Coffee | 50 | 200 | 250 |
| Tea | 100 | 150 | 250 |
| Soft Drink | 200 | 200 | 400 |
| Other | 50 | 50 | 100 |
| 400 | 600 | 1000 |
We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is
| a. .33. |
| b. 200. |
| c. .25. |
| d. 150. |
58. Marascuilo procedure is used to test for a significant difference between pairs of population
| a. variances. |
| b. standard deviations. |
| c. means. |
| d. proportions. |
59. You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.
| 2 | 3 | 5 | 5 | 7 | 8 | 8 | 9 | 9 | 10 |
| 11 | 11 | 12 | 12 | 12 | 12 | 13 | 13 | 13 | 14 |
| 15 | 15 | 15 | 16 | 16 | 17 | 17 | 18 | 18 | 19 |
The number of intervals or categories used to test the hypothesis for this problem is
| a. 5. |
| b. 6. |
| c. 10. |
| d. 4. |
60. With respect to the number of categories, k, when would a multinomial experiment be identical to a binomial experiment?
| a. k = 1 |
| b. k = 2 |
| c. k = 3 |
| d. k = 4 |
61. An important application of the chi-square distribution is
| a. testing for goodness of fit. |
| b. testing for the independence of two categorical variables. |
| c. making inferences about a single population variance. |
| d. All of these alternatives are correct. |
62. In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The calculated value for the test statistic equals
| a. .01. |
| b. 4.38. |
| c. .75. |
| d. 4.29. |
63. The sampling distribution for a goodness of fit test is the
| a. t distribution. |
| b. chi-square distribution. |
| c. normal distribution. |
| d. Poisson distribution. |
64. The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
| Political Party | Support |
| Democrats | 100 |
| Republicans | 120 |
| Independents | 80 |
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The calculated value for the test statistic equals
| a. 2. |
| b. 0. |
| c. 8. |
| d. 4. |
65. In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals
| a. 9.348. |
| b. 5.991. |
| c. 7.378. |
| d. 7.815. |
66. If there are three or more populations, then it is
| a. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations. |
| b. possible to test for equality of three or more population proportions. |
| c. reasonable to test for equality of multiple population proportions using chi-square lower tail tests. |
| d. customary to use a t distribution to test for equality of the three population proportions. |
67. The table below gives beverage preferences for random samples of teens and adults.
| Teens | Adults | Total | |
| Coffee | 50 | 200 | 250 |
| Tea | 100 | 150 | 250 |
| Soft Drink | 200 | 200 | 400 |
| Other | 50 | 50 | 100 |
| 400 | 600 | 1000 |
We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The test statistic for this test of independence is
| a. 0. |
| b. 62.5. |
| c. 82.5. |
| d. 8.4 |
68. The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
| Political Party | Support |
| Democrats | 100 |
| Republicans | 120 |
| Independents | 80 |
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The number of degrees of freedom associated with this problem is
| a. 299. |
| b. 300. |
| c. 2. |
| d. 3. |
69. The test for goodness of fit
| a. is always a two-tailed test. |
| b. is always an upper tail test. |
| c. is always a lower tail test. |
| d. can be a lower or an upper tail test. |
70. Which function in Excel is used to perform a test of independence?
| a. CHISQ.TEST |
| b. T.TEST |
| c. NORM.S.DIST |
| d. Z.TEST |
71. A manufacturer of carpentry screws claims that its production machine is very accurate and that the standard deviation of the length of all screws produced is .08 mm or less. A sample of 30 screws showed a standard deviation of .10. The test statistic to test the manufacturer’s claim is _____.
| a. 18.56 |
| b. 19.2 |
| c. 45.31 |
| d. 23.2 |
72. We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is
| a. σ2 ≥ 49. |
| b. σ < 49. |
| c. σ < 7. |
| d. σ2 ≥ 7. |
73. The symbol used for the variance of the sample is
| a. s2. |
| b. σ. |
| c. σ2. |
| d. s. |
74. The value of F.05 with 8 numerator and 19 denominator degrees of freedom is
| a. 2.48. |
| b. 2.58. |
| c. 2.96. |
| d. 3.63. |
75. Which of the following has an F distribution?
a.  |
b.  |
c.  |
d.  |
76. A researcher would like to test the hypothesis that population B has a smaller variance than population A, using a 5% level of significance for the hypothesis test. What is the critical value from the F distribution table?
| a. 2.39 |
| b. 2.84 |
| c. 2.22 |
| d. 1.96 |
77. The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is
| a. 16.42 to 194.35. |
| b. 243.086 to 453.520. |
| c. 254.419 to 429.203. |
| d. 14.14 to 174.94. |
78. We are interested in testing whether the variance of a population is significantly more than 625. The null hypothesis for this test is
| a. H0: σ2 ≤ 625. |
| b. H0: σ2 > 625. |
| c. H0: σ2 ≤ 25. |
| d. H0: σ2 ≥ 625. |
79. For a sample size of 21 at 95% confidence, the chi-square values needed for interval estimation are
| a. 10.283 and 35.479. |
| b. 2.700 and 19.023. |
| c. 8.260 and 37.566. |
| d. 9.591 and 34.170 |
80. The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is .1 ounces or less. A sample of 20 bottles showed a standard deviation of .11 ounces. The test statistic to test the claim is
| a. 2.3. |
| b. 22.99. |
| c. 4.85. |
| d. 24.2. |
81. The critical value of F using α = .05 when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is
| a. 2.10. |
| b. 2.45. |
| c. 2.94. |
| d. 2.37. |
82. The chi-square value for a one-tailed (lower tail) test when the level of significance is .1 and the sample size is 15 is
| a. 23.685. |
| b. 7.790. |
| c. 21.064. |
| d. 6.571. |
83. Consider the following hypothesis problem.
| n = 30 | H0: σ2 = 500 |
| s2 = 625 | Ha: σ2 ≠ 500 |
The test statistic equals
| a. 37.50. |
| b. 23.20. |
| c. 24.00. |
| d. 36.25. |
84. A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is
| a. 100.75. |
| b. 51.25. |
| c. 50. |
| d. 10 |
85. The value of F.05 with 8 numerator and 19 denominator degrees of freedom is
| a. 2.48. |
| b. 2.96. |
| c. 3.63. |
| d. 2.58. |
86. χ2.975 = 8.231 indicates that
| a. 2.5% of the chi-square values are greater than 8.231. |
| b. 97.5% of the chi-square values are greater than 8.231. |
| c. 5% of the chi-square values are equal to 8.231. |
| d. 97.5% of the chi-square values are less than 8.231 |
87. Consider the following sample information from Population A and Population B.
| Sample A | Sample B | |
| n | 24 | 16 |
| s2 | 32 | 38 |
We want to test the hypothesis that the population variances are equal. The test statistic for this problem equals
| a. 1.19. |
| b. 1.50. |
| c. .84. |
| d. .67. |
88. Given the sample information below, what test statistic should be used to determine whether the standard deviations are equal for two populations, prior to performing a hypothesis test for the equality of the population means?
| a. t = 18.75, with degrees of freedom = 19 |
| b. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29 |
| c. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19 |
| d. F = 0.40, with degrees of freedom = 19 |
89. Consider the following hypothesis problem.
| n = 23 | s2 = 60 | H0: σ2 ≤ 66 |
| Ha: σ2 > 66 |
The p-value is
| a. between .05 and .10. |
| b. less than .025. |
| c. between .025 and .05. |
| d. greater than .10. |
90. The sampling distribution used when making inferences about a single population’s variance is
| a. a normal distribution. |
| b. a t distribution. |
| c. a chi-square distribution. |
| d. an F distribution. |
91. The value of F.01 with 9 numerator and 20 denominator degrees of freedom is
| a. 2.91. |
| b. 2.94. |
| c. 2.39. |
| d. 3.46. |
92. Which of the following is not a property of a chi-square distribution?
| a. χ2 is skewed to the right. |
| b. The number of degrees of freedom defines the shape of the distribution of χ2. |
| c. χ2 can have both positive and negative values. |
| d. All of these choices are properties of the χ2 distribution. |
93. A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is
| a. 10. |
| b. 51.25. |
| c. 50. |
| d. 100.75. |
94. Which of the following rejection rules is proper?
| a. Reject H0 if p-value ≥ α/2. |
| b. Reject H0 if F ≥ Fα. |
| c. Reject H0 if F ≤ Fα/2. |
| d. Reject H0 if p-value ≤ Fα. |
95. In practice, the most frequently encountered hypothesis test about a population variance is a
| a. one-tailed test, with rejection region in the lower tail. |
| b. two-tailed test, with equal-size rejection regions. |
| c. two-tailed test, with unequal-size rejection regions. |
| d. one-tailed test, with rejection region in the upper tail. |
96. What is the null hypothesis for testing whether the variance of a population differs from 2.5?
a.  |
b.  |
c.  |
d.  |
97. The critical value of F using α = .05 when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is
| a. 2.45. |
| b. 2.10. |
| c. 2.94. |
| d. 2.37. |
98. What is the critical value of F for a one-tailed test at the α=.10 level, when there is a sample size of 8 for the sample with the smaller variance and a sample size of 11 for the sample with the larger sample variance?
| a. 2.70 |
| b. 2.41 |
| c. 1.65 |
| d. 3.64 |
99. We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is
| a. σ2 ≥ 49. |
| b. σ2 ≥ 7. |
| c. σ < 7. |
| d. σ < 49. |
100. Which of the following has a chi-square distribution?
| a. (n – 1)s/σ. |
| b. (n – 1)s2/σ2. |
| c. (n – 1)σ2/s2. |
| d. (n – 1)σ/s. |
101. The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is
| a. 16.42 to 194.35. |
| b. 254.419 to 429.203. |
| c. 14.14 to 174.94. |
| d. 243.086 to 453.520. |
102. The value of F.01 with 9 numerator and 20 denominator degrees of freedom is
| a. 2.91. |
| b. 3.46. |
| c. 2.39. |
| d. 2.94. |
103. To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let the
| a. sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic. |
| b. smaller sample variance be the numerator of the test statistic. |
| c. larger sample variance be the numerator of the test statistic. |
| d. sample variance from the population with the larger hypothesized variance be the numerator of the test statistic. |
104. The value of F.05 with 8 numerator and 19 denominator degrees of freedom is
| a. 2.58. |
| b. 2.48. |
| c. 2.96. |
| d. 3.63. |
105. The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. At the .05 level of significance, the null hypothesis
| a. should not be tested. |
| b. should not be rejected. |
| c. should be rejected. |
| d. should be revised. |
106. A manufacturer of carpentry screws claims that its production machine is very accurate and that the standard deviation of the length of all screws produced is .08 mm or less. A sample of 30 screws showed a standard deviation of .10. The test statistic to test the manufacturer’s claim is _____.
| a. 19.2 |
| b. 45.31 |
| c. 23.2 |
| d. 18.56 |
107. A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is
| a. 50. |
| b. 5. |
| c. 21. |
| d. 20 |
108. A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are
| a. 15.308 and 44.461. |
| b. 11.808 and 49.645. |
| c. 16.151 and 40.113. |
| d. 14.573 and 43.195. |
109. The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is .1 ounces or less. A sample of 20 bottles showed a standard deviation of .11 ounces. The test statistic to test the claim is
| a. 2.3. |
| b. 4.85. |
| c. 22.99. |
| d. 24.2 |
110. A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is
| a. 20. |
| b. 50. |
| c. 21. |
| d. 5. |
111. To avoid the problem of not having access to Tables of F distribution when F values are needed for the lower tail, the numerator of the test statistic for a two-tailed test should be the one with
| a. the larger sample size. |
| b. the larger sample variance. |
| c. the smaller sample variance. |
| d. the smaller sample size |
112. Consider the following sample information from Population A and Population B.
| Sample A | Sample B | |
| n | 24 | 16 |
| s2 | 32 | 38 |
We want to test the hypothesis that the population variances are equal. The test statistic for this problem equals
| a. 1.19. |
| b. 1.50. |
| c. .67. |
| d. .84. |
113. In practice, the most frequently encountered hypothesis test about a population variance is a
| a. one-tailed test, with rejection region in the upper tail. |
| b. one-tailed test, with rejection region in the lower tail. |
| c. two-tailed test, with unequal-size rejection regions. |
| d. two-tailed test, with equal-size rejection regions. |
114. A sample of 21 elements is selected to estimate a 90% confidence interval for the variance of the population. The chi-square value(s) to be used for this interval estimation is(are)
| a. 12.443 and 28.412. |
| b. 10.851 and 31.410. |
| c. 31.410. |
| d. 12.443. |
115. Consider the following hypothesis problem.
| n = 14 | H0: σ2 ≤ 410 |
| s = 20 | Ha: σ2 > 410 |
The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)
| a. 5.009 and 24.736. |
| b. 5.629 and 26.119. |
| c. 23.685. |
| d. 22.362. |
116. consider the scenario where
The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the table is(are) _____.
| a. 6.262 and 27.488 |
| b. 27.488 |
| c. 5.629 and 26.119 |
| d. 5.629 |
117. A sample of 60 items from population 1 has a sample variance of 8 while a sample of 40 items from population 2 has a sample variance of 10. If we want to test whether the variances of the two populations are equal, the test statistic will have a value of
| a. 1.56. |
| b. .8. |
| c. 1.25. |
| d. 1.5 |
118.
the manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 6 minutes. A 95% confidence interval estimate for the standard deviation of the service times (in minutes) for all their new automobiles is
| a. 4.778 to 8.066. |
| b. 22.833 to 65.059. |
| c. 16.047 to 45.722. |
| d. 2.93 to 6.31. |
119. Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year’s student body showed the following number of students in each classification.
| Freshmen | 83 |
| Sophomores | 68 |
| Juniors | 85 |
| Seniors | 64 |
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The calculated value for the test statistic equals
| a. 1.66. |
| b. .65. |
| c. .54. |
| d. 6.66. |
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