- 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 p-value is
| a. between .05 and .1. |
| b. greater than .1. |
| c. between .025 and .05. |
| d. less than .01. |
2. Which of the following Chi-Square tests can be used to determine if a data set follows a Normal distribution?
| a. Chi-Square Goodness of Fit |
| b. Chi Square Test of Association |
| c. Chi-Square Test of Equality of Three or More Population Proportions |
| d. Chi-Square Test of Homogeneity |
3. 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 number of freshmen is
| a. 83. |
| b. 90. |
| c. 30. |
| d. 10. |
4. 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 calculated value for the test statistic equals
| a. 6. |
| b. 2. |
| c. 1.67. |
| d. 0. |
5. The test for goodness of fit
| a. is always an upper tail test. |
| b. is always a two-tailed test. |
| c. is always a lower tail test. |
| d. can be a lower or an upper tail test. |
6. The degrees of freedom for a table with 6 rows and 3 columns is
| a. 10. |
| b. 18. |
| c. 15. |
| d. 6. |
7. 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. multinomial population. |
| c. Marascuilo procedure. |
| d. test for independence. |
8. The number of degrees of freedom associated with the chi-square distribution in a test of independence is
| a. number of sample items minus 1. |
| b. number of populations minus 1. |
| c. number of populations minus number of estimated parameters minus 1. |
| d. number of rows minus 1 times number of columns minus 1. |
9. 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. |
10. 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. With a .05 level of significance, the critical value for the test is
| a. 15.507. |
| b. 7.815. |
| c. 14.067. |
| d. 5.991. |
11. 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 number of freshmen is
| a. 30. |
| b. 83. |
| c. 90. |
| d. 10. |
12. 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 calculated value for the test statistic equals
| a. 1.67. |
| b. 2. |
| c. 6. |
| d. 0. |
13. In order not to violate the requirements necessary to use the chi-square distribution for testing equality of three or more population proportions, each expected frequency in a goodness of fit test must be
| a. no more than 5. |
| b. at least 5. |
| c. less than 2. |
| d. at least 10 |
14. 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 expected frequency for each group is
| a. .333. |
| b. .50. |
| c. 1/3. |
| d. 50. |
15. If the sample size is n = 75, what are the degrees of freedom for the appropriate chi-square distribution when testing for independence of two variables each with three categories?
| a. 74 |
| b. 4 |
| c. 2 |
| d. 69 |
16. 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. 7.815. |
| b. 5.991. |
| c. 7.378. |
| d. 9.348 |
17. 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. was designed wrong. |
| b. should not be rejected. |
| c. cannot be tested. |
| d. should be rejected. |
18. 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. 100. |
| d. .50. |
19. A random sample of 550 physicians was selected and classified according to the type of practice they operate and whether or not their practice was full (meaning, not accepting new patients). The counts are given in the table below.
The test statistic for a test of independence is χ2 = 34.893. What is the p-value for this test?
| a. p = .004 |
| b. p = .0025 |
| c. p = .05 |
| d. p < .0001 |
20. An important application of the chi-square distribution is
| a. making inferences about a single population variance. |
| b. testing for the independence of two categorical variables. |
| c. testing for goodness of fit. |
| d. All of these alternatives are correct. |
21. How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?
| a. 7 |
| b. 62 |
| c. 9 |
| d. 74 |
22. 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. .50. |
| b. .333. |
| c. 100. |
| d. 50. |
23. 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. 150. |
| b. .25. |
| c. .33. |
| d. 200 |
24. 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. 8.4. |
| c. 82.5. |
| d. 62.5. |
25. 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. Marascuilo procedure. |
| d. multinomial population. |
26. The degrees of freedom for a data table with 10 rows and 11 columns is
| a. 90. |
| b. 21. |
| c. 100. |
| d. 110. |
27. 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. customary to use a t distribution to test for equality of the three population proportions. |
| c. reasonable to test for equality of multiple population proportions using chi-square lower tail tests. |
| d. possible to test for equality of three or more population proportions. |
28. 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. 3.11. |
| c. .18. |
| d. 2.89. |
29. Which function in Excel is used to perform a test of independence?
| a. Z.TEST |
| b. CHISQ.TEST |
| c. T.TEST |
| d. NORM.S.DIST |
30. A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a
| a. probability test. |
| b. comparison test. |
| c. goodness of fit test. |
| d. normality test. |
31. 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. multinomial population. |
| b. test for independence. |
| c. Marascuilo procedure. |
| d. z test for proportions. |
32. The number of categorical outcomes per trial for a multinomial probability distribution is
| a. four or more. |
| b. two or more. |
| c. three or more. |
| d. five or more. |
33. If there are three or more populations, then it is
| a. reasonable to test for equality of multiple population proportions using chi-square lower tail tests. |
| b. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations. |
| c. possible to test for equality of three or more population proportions. |
| d. customary to use a t distribution to test for equality of the three population proportions |
34. 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 expected frequency for each group is
| a. 1/3. |
| b. .50. |
| c. 50. |
| d. .333. |
35. The properties of a multinomial experiment include all of the following except
| a. the experiment consists of a sequence of n identical trials. |
| b. the probability of each outcome can change from trial to trial. |
| c. the trials are independent. |
| d. three or more outcomes are possible on each trial. |
36. In order not to violate the requirements necessary to use the chi-square distribution for testing equality of three or more population proportions, each expected frequency in a goodness of fit test must be
| a. less than 2. |
| b. at least 10. |
| c. no more than 5. |
| d. at least 5. |
37. A random sample of 100 high school students was surveyed regarding their favorite subject. The following counts were obtained:
The researcher conducted a test to determine whether the proportion of students was equal for all four subjects. What is the value of the test statistic?
| a. 25 |
| b. 6 |
| c. 0 |
| d. –4 |
38. The test statistic for goodness of fit has a chi-square distribution with k – 1 degrees of freedom provided that the expected frequencies for all categories are
| a. 5 or more. |
| b. 10 or more. |
| c. 2k. |
| d. k or more |
39. 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. With a .05 level of significance, the critical value for the test is
| a. 5.991. |
| b. 15.507. |
| c. 14.067. |
| d. 7.815. |
40. Marascuilo procedure is used to test for a significant difference between pairs of population
| a. proportions. |
| b. means. |
| c. variances. |
| d. standard deviations. |
41. 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 is uniform. |
| c. distribution might have been normal. |
| d. null hypothesis cannot be rejected. |
42. 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 p-value is
| a. between .05 and .1. |
| b. between .025 and .05. |
| c. less than .01. |
| d. greater than .1. |
43. 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 = 0.40, with degrees of freedom = 19 |
| c. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29 |
| d. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19 |
44. 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. 50. |
| b. 100.75. |
| c. 51.25. |
| d. 10. |
45. 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. 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 lower tail. |
46. A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is
| a. 21. |
| b. 5. |
| c. 50. |
| d. 20. |
47. Consider the following hypothesis problem.
| n = 14 | H0: σ2 ≤ 410 |
| s = 20 | Ha: σ2 > 410 |
At the 5% level of significance, the null hypothesis
| a. should not be rejected. |
| b. should be revised. |
| c. should be rejected. |
| d. should not be tested. |
48. 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. F distribution. |
| d. t distribution |
49. 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. |
50. Which of the following has an F distribution?
| a. s1/s2. |
| b. (n – 1)s1/s2. |
| c. (n – 1)s/σ. |
| d. s12/s22. |
51. A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a
| a. goodness of fit test. |
| b. normality test. |
| c. comparison test. |
| d. probability test. |
52. 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. .54. |
| b. 6.66. |
| c. .65. |
| d. 1.66. |
53. 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. 3. |
| d. 2 |
54. 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. .3. |
| b. 90. |
| c. .35. |
| d. 105. |
55. Which function in Excel is used to perform a test of independence?
| a. T.TEST |
| b. Z.TEST |
| c. NORM.S.DIST |
| d. CHISQ.TEST |
56. An important application of the chi-square distribution is
| a. making inferences about a single population variance. |
| b. testing for goodness of fit. |
| c. testing for the independence of two categorical variables. |
| d. All of these alternatives are correct. |
57. How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?
| a. 62 |
| b. 7 |
| c. 9 |
| d. 74 |
58. 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 p-value is
| a. between .025 and .05. |
| b. less than .005. |
| c. greater than .1. |
| d. between .05 and .1. |
59. The 99% confidence interval estimate for a population variance when a sample standard deviation of 12 is obtained from a sample of 10 items is
| a. 4.589 to 62.253. |
| b. 54.941 to 746.974. |
| c. 62.042 to 562.895. |
| d. 46.538 to 422.171. |
60. 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. 50. |
| b. 10. |
| c. 51.25. |
| d. 100.75. |
61. 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 be revised. |
| b. should not be rejected. |
| c. should be rejected. |
| d. should not be tested. |
62. We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is
| a. H0: σ2 < 1.44. |
| b. H0: σ < 1.20. |
| c. H0: σ2 ≥ 1.44. |
| d. H0: s2 ≥ 1.44. |
63. 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. less than .10. |
| b. zero. |
| c. .05. |
| d. greater than .10. |
64. 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. 2.11. |
| b. 2.29. |
| c. 2.13. |
| d. 2.24. |
65. Which of the following rejection rules is proper?
| a. Reject H0 if p-value ≥ α/2. |
| b. Reject H0 if F ≤ Fα/2. |
| c. Reject H0 if p-value ≤ Fα. |
| d. Reject H0 if F ≥ Fα. |
66. Which of the following rejection rules is proper?
| a. Reject H0 if p-value ≥ α/2. |
| b. Reject H0 if F ≤ Fα/2. |
| c. Reject H0 if p-value ≤ Fα. |
| d. Reject H0 if F ≥ Fα. |
67. 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. 2.144 to 9.948. |
| c. 2.93 to 6.31. |
| d. 9.46 to 34.09. |
68. We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is
| a. H0: σ < 1.20. |
| b. H0: s2 ≥ 1.44. |
| c. H0: σ2 < 1.44. |
| d. H0: σ2 ≥ 1.44. |
69. The χ2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 20 is _____.
| a. 31.410 |
| b. 10.851 |
| c. 10.117 |
| d. 30.144 |
70. 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 not be tested. |
| b. should be rejected. |
| c. should not be rejected. |
| d. should be revised |
71. 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. 1.65 |
| b. 3.64 |
| c. 2.70 |
| d. 2.41 |
72. 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 |
At the 5% level of significance, the conclusion of the test is that the
| a. sample data has no probability distribution. |
| b. null hypothesis cannot be rejected. |
| c. data does not follow a normal distribution. |
| d. sample data is incorrect. |
73. A random sample of 550 physicians was selected and classified according to the type of practice they operate and whether or not their practice was full (meaning, not accepting new patients). The counts are given in the table below.
The test statistic for a test of independence is χ2 = 34.893. What is the p-value for this test?
| a. p = .05 |
| b. p = .0025 |
| c. p < .0001 |
| d. p = .004 |
74. A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a
| a. comparison test. |
| b. normality test. |
| c. goodness of fit test. |
| d. probability test. |
75. 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 calculated value for the test statistic equals
| a. 2. |
| b. 6. |
| c. 1.67. |
| d. 0. |
76. How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?
| a. 62 |
| b. 9 |
| c. 74 |
| d. 7 |
77. A population where each of its element is assigned to one and only one of several classes or categories is a
| a. normal population. |
| b. multinomial population. |
| c. binomial population. |
| d. Poisson population. |
78. 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. .18. |
| b. 2.89. |
| c. 3.11. |
| d. 1.72. |
79. If there are three or more populations, then it is
| a. possible to test for equality of three or more population proportions. |
| b. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations. |
| 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. |
80. 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. .33. |
| d. 150. |
81. 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: the proportions are not all equal. |
| b. H0: p1= .10, p2 = .30, p3 = .50, p4 = .10 |
| c. H0: p1 = .25, p2 = .25, p3 = .25, p4 = .25 |
| d. H0: p = .50 |
82. The test for goodness of fit
| a. can be a lower or an upper tail test. |
| b. is always a lower tail test. |
| c. is always an upper tail test. |
| d. is always a two-tailed test |
83. A random sample of 100 high school students was surveyed regarding their favorite subject. The following counts were obtained:
The researcher conducted a test to determine whether the proportion of students was equal for all four subjects. What is the value of the test statistic?
| a. 0 |
| b. –4 |
| c. 25 |
| d. 6 |
84. If the sample size is n = 75, what are the degrees of freedom for the appropriate chi-square distribution when testing for independence of two variables each with three categories?
| a. 74 |
| b. 2 |
| c. 4 |
| d. 69 |
85. 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. should not be rejected. |
| b. should be rejected. |
| c. was designed wrong. |
| d. cannot be tested. |
86. The number of categorical outcomes per trial for a multinomial probability distribution is
| a. three or more. |
| b. two or more. |
| c. five or more. |
| d. four or more. |
87. 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. 7.378. |
| c. 7.815. |
| d. 5.991. |
88. 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. .75. |
| c. 4.38. |
| d. 4.29. |
89. The properties of a multinomial experiment include all of the following except
| a. the experiment consists of a sequence of n identical trials. |
| b. the trials are independent. |
| c. three or more outcomes are possible on each trial. |
| d. the probability of each outcome can change from trial to trial. |
90. 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. 105. |
| b. 90. |
| c. .3. |
| d. .35. |
91. How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?
| a. 62 |
| b. 74 |
| c. 7 |
| d. 9 |
92. 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. 8. |
| b. 0. |
| c. 2. |
| d. 4 |
93. 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. |
94. 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 might have been normal. |
| b. null hypothesis cannot be rejected. |
| c. Marascuilo procedure is more applicable. |
| d. distribution is uniform. |
95. 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 p-value is
| a. less than .01. |
| b. between .05 and .1. |
| c. between .01 and .05. |
| d. larger than .1 |
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