1. The parameter(s) of the chi-square distribution is/are:
A) the sample size B) degrees of freedom C) n and x D) n, x, and p
2. For a chi-square distribution curve with 3 or more degrees of freedom, the peak occurs at
the point:
A) x = 10 C) x = degrees of freedom minus 2
B) x = degrees of freedom minus 1 D) n – x
3. A chi-square distribution assumes:
A) negative values only C) nonnegative values only
B) positive values only D) all values
4. For small degrees of freedom, the chi-square distribution is:
A) symmetric B) skewed to the right C) skewed to the left D) rectangular
5. For very large degrees of freedom, the chi-square distribution becomes:
A) symmetric B) skewed to the right C) skewed to the left D) rectangular
6. What is the chi-square value for 14 degrees of freedom and a .05 area in the right tail?
A) 21.604 B) 26.119 C) 23.685 D) 29.141
7. What is the chi-square value for 9 degrees of freedom and a .01 area in the left tail?
A) 21.666 B) -21.666 C) 2.088 D) -2.088
8. What is the chi-square value for 19 degrees of freedom and a 0.025 area in the right tail?
A) 30.144 B) 32.852 C) 8.907 D) 10.117
Chapter 11
9. What is the chi-square value for 12 degrees of freedom and a 0.10 area in the left tail?
A) 6.304 B) -6.304 C) 18.549 D) –18.549
10. Which of the following is not a characteristic of a multinomial experiment?
A) It consists of two identical trials.
B) Each trial results in one of the k possible outcomes where k is a number greater
than 2.
C) The trials are independent.
D) The probabilities of various outcomes remain constant for each trial.
11. Which of the following is not a characteristic of a multinomial experiment?
A) It consists of n identical trials.
B) Each trial results in one of two possible outcomes.
C) The trials are independent.
D) The probabilities of various outcomes remain constant for each trial.
12. Which of the following is not a characteristic of a multinomial experiment?
A) It consists of n identical trials.
B) Each trial results in one of the k possible outcomes where k is a number greater
than 2.
C) The trials are dependent.
D) The probabilities of various outcomes remain constant for each trial.
13. Which of the following is not a characteristic of a multinomial experiment?
A) It consists of n identical trials.
B) Each trial results in one of the k possible outcomes where k is a number greater
than 2.
C) The trials are independent.
D) The probabilities of various outcomes are different for each trial.
Chapter 11
14. For a goodness-of-fit test, the frequencies obtained from the performance of an
experiment are the:
A) expected frequencies C) objective frequencies
B) subjective frequencies D) observed frequencies
15. For a goodness-of-fit test, the frequencies that we would obtain if the null hypothesis is
true are the:
A) expected frequencies C) objective frequencies
B) subjective frequencies D) observed frequencies
16. For a goodness-of-fit test with the number of categories equal to k and sample size equal
to n, the degrees of freedom are:
A) k – 2 B) n – k C) k – n D) k – 1
17. For a goodness-of-fit test, when n is the sample size and p is the probability of a category
occurring, we calculate the expected frequency for a category by:
A)
E np=
B)
E xp=
C)
E nx=
D)
E nkp=
18. For a goodness-of-fit test, the sample size should be large enough so that the:
A) observed frequency for each category is at least 10
B) expected frequency for each category is at least 10
C) observed frequency for each category is at least 5
D) expected frequency for each category is at least 5
19. A goodness-of-fit test:
A) is always a right-tailed test
B) is always a left-tailed test
C) is always a two-tailed test
D) can be a right-tailed, left-tailed, or a two-tailed test
Chapter 11
Use the following to answer questions 20-24:
The table below lists the observed frequencies for all four categories for an experiment.
Category
Observed Frequency
1
12
2
18
3
14
4
16
20. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the four categories is the same. What is the expected
frequency for the second category?
21. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the four categories is the same. The expected
frequencies for the four categories are:
22. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the four categories is the same. What are the degrees
of freedom for this test?
23. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the four categories is the same. The significance
level is 1%. What is the critical value of chi-square?
A) 13.277 B) 11.345 C) 12.838 D) 14.860
Chapter 11
24. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the four categories is the same. What is the value of
the test statistic, rounded to three decimal places?
Use the following to answer questions 25-29:
The table below lists the observed frequencies for all four categories for an experiment.
Category
Observed Frequency
1
23
2
5
3
41
4
11
25. The null hypothesis for the goodness-of-fit test is that 40% of all elements of the
population belong to the first category, 30% belong to the second category, 20% belong
to the third category, and 10% belong to the fourth category. What is the expected
frequency for the fourth category?
26. The null hypothesis for the goodness-of-fit test is that 40% of all elements of the
population belong to the first category, 30% belong to the second category, 20% belong
to the third category, and 10% belong to the fourth category. The expected frequencies
for the four categories are:
27. The null hypothesis for the goodness-of-fit test is that 40% of all elements of the
population belong to the first category, 30% belong to the second category, 20% belong
to the third category, and 10% belong to the fourth category. What are the degrees of
freedom for this test?
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28. The null hypothesis for the goodness-of-fit test is that 40% of all elements of the
population belong to the first category, 30% belong to the second category, 20% belong
to the third category, and 10% belong to the fourth category. The significance level is
10%. What is the critical value of chi-square?
A) 9.488 B) 7.815 C) 7.779 D) 6.251
29. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the four categories is the same. What is the value of
the test statistic, rounded to three decimal places?
Use the following to answer questions 30-34:
The table below lists the observed frequencies for all four categories for an experiment.
Category
Observed Frequency
1
39
2
13
3
15
4
19
5
14
30. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the five categories is the same. What is the expected
frequency for the fourth category?
31. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the five categories is the same. The expected
frequencies for the five categories are:
Chapter 11
32. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the five categories is the same. What are the degrees
of freedom for this test?
33. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the five categories is the same. The significance
level is 5%. What is the critical value of chi-square?
A) 11.070 B) 12.833 C) 11.143 D) 9.488
34. The null hypothesis for the goodness-of-fit test is that the proportion of all elements of
the population that belong to each of the five categories is the same. What is the value of
the test statistic, rounded to three decimal places?
Use the following to answer questions 35-39:
You ask 100 persons what color of car they like the most. The table below lists the observed
frequencies for such a survey.
Color
Observed Frequency
Black
22
Blue
29
Red
14
White
5
Other
30
35. The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars,
25% like blue cars, 20% like red cars, 10% like white cars, and 35% like other colors.
What is the expected frequency for red cars?
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36. The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars,
25% like blue cars, 20% like red cars, 10% like white cars, and 35% like other colors.
The expected frequencies for the various colors are:
37. The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars,
25% like blue cars, 20% like red cars, 10% like white cars, and 35% like other colors.
What are the degrees of freedom for this test?
38. The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars,
25% like blue cars, 20% like red cars, 10% like white cars, and 35% like other colors.
The significance level is 2.5%. What is the critical value of chi-square?
A) 9.488 B) 11.143 C) 12.833 D) 11.070
39. The null hypothesis for the goodness-of-fit test is that 10% of all persons like black cars,
25% like blue cars, 20% like red cars, 10% like white cars, and 35% like other colors.
What is the value of the test statistic, rounded to three decimal places?
Use the following to answer questions 40-44:
The table below lists the number of crimes reported at a police station on each day of the week
for the past three months.
Day of the Week
Number of Crimes
Monday
21
Tuesday
10
Wednesday
13
Thursday
16
Friday
25
Saturday
29
Sunday
26
Chapter 11
40. The null hypothesis for the goodness-of-fit test is that the number of crimes reported at
this police station is the same for each day of the week. What is the expected number of
crimes reported on a Thursday?
41. The null hypothesis for the goodness-of-fit test is that the number of crimes reported at
this police station is the same for each day of the week. The expected frequencies for
each of the seven days are:
42. The null hypothesis for the goodness-of-fit test is that the number of crimes reported at
this police station is the same for each day of the week. What are the degrees of freedom
for this test?
43. The null hypothesis for the goodness-of-fit test is that the number of crimes reported at
this police station is the same for each day of the week. The significance level is 10%.
What is the critical value of chi-square?
A) 12.017 B) 14.067 C) 10.645 D) 12.592
44. The null hypothesis for the goodness-of-fit test is that the number of crimes reported at
this police station is the same for each day of the week. What is the value of the test
statistic?
Chapter 11
45. For a chi-square test of independence, what are the degrees of freedom?
A) sample size minus one
B) sample size minus two
C) (R-1)(C-1) where R is the number of rows and C is the number of columns in the
contingency table
D) (n-1)(k-1) where n is the sample size and k is the number of categories
46. For a chi-square test of homogeneity, what are the degrees of freedom?
A) sample size minus one
B) sample size minus two
C) (R-1)(C-1) where R is the number of rows and C is the number of columns in the
contingency table
D) (n-1)(k-1) where n is the sample size and k is the number of categories
47. A chi-square test of independence:
A) is always a right-tailed test
B) is always a left-tailed test
C) is always a two-tailed test
D) can be a right-tailed, a left-tailed, or a two-tailed test
48. A chi-square test of homogeneity:
A) is always a right-tailed test
B) is always a left-tailed test
C) is always a two-tailed test
D) can be a right-tailed, a left-tailed, or a two-tailed test
49. A chi-square test of independence is about the independence of:
A) two means
B) two proportions
C) two characteristics presented in a contingency table
D) means of several populations
50. A chi-square test of homogeneity is about:
A) testing the null hypothesis that two samples are homogeneous
B) testing the null hypothesis that two proportions are homogeneous
C) the independence of two characteristics presented in a contingency table
D) testing the null hypothesis that the proportions of elements with certain
characteristics in two or more different populations are the same
Chapter 11
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51. For a chi-square test of independence, a contingency table with 2 rows and 2 columns has
how many degrees of freedom?
52. For a chi-square test of independence, a contingency table with 7 rows and 8 columns has
how many degrees of freedom?
53. For a chi-square test of homogeneity, a contingency table with 5 rows and 6 columns has
how many degrees of freedom?
54. For a chi-square test of homogeneity, a contingency table with 7 rows and 9 columns has
how many degrees of freedom?
Use the following to answer questions 55-61:
You observe 100 randomly selected college students to find out whether they arrive on time or
late for their classes. The table below gives a two-way classification for these students.
Gender
On Time
Late
Female
35
9
Male
43
13
55. For a chi-square test of independence for this contingency table, what is the number of
degrees of freedom?
56. For a chi-square test of independence for this contingency table, what are the observed
frequencies for the first row?
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Page 12
57. For a chi-square test of independence for this contingency table, what are the expected
frequencies for the first row, rounded to two decimal places?
58. For a chi-square test of independence for this contingency table, what are the observed
frequencies for the second column?
59. For a chi-square test of independence for this contingency table, what are the expected
frequencies for the second column, rounded to two decimal places?
60. To perform a chi-square test of independence for this contingency table at the 1%
significance level, what is the critical value of chi-square?
A) 7.879 B) 6.635 C) 10.597 D) 9.210
61. To perform a chi-square test of independence for this contingency table, what is the value
of the chi-square test statistic (rounded to three decimal places)?
Use the following to answer questions 62-68:
You ask 600 randomly selected working adults whether or not they are satisfied with their jobs.
The table below gives a two-way classification for these adults.
Gender
Satisfied
Not Satisfied
Female
192
94
Male
240
74
Chapter 11
62. For a chi-square test of independence for this contingency table, what is the number of
degrees of freedom?
63. For a chi-square test of independence for this contingency table, what are the observed
frequencies for the second row?
64. For a chi-square test of independence for this contingency table, what are the expected
frequencies for the second row, rounded to two decimal places?
65. For a chi-square test of independence for this contingency table, what are the observed
frequencies for the first column?
66. For a chi-square test of independence for this contingency table, what are the expected
frequencies for the first column, rounded to two decimal places?
67. To perform a chi-square test of independence for this contingency table at the 5%
significance level, what is the critical value of chi-square?
A) 5.991 B) 7.378 C) 3.841 D) 5.024
68. To perform a chi-square test of independence for this contingency table, what is the value
of the chi-square test statistic (rounded to three decimal places)?
Chapter 11
Use the following to answer questions 69-75:
A clinic administers two drugs to two groups of randomly assigned patients to cure the same
disease: 70 patients received Drug I and 80 patients received Drug II. The following table gives
the information about the numbers of patients cured and those not cured by each of these two
drugs.
Drug
Cured
Not Cured
I
60
10
II
59
21
69. For a chi-square test of homogeneity for this contingency table, what is the number of
degrees of freedom?
70. For a chi-square test of homogeneity for this contingency table, what are the observed
frequencies for the first row?
71. For a chi-square test of homogeneity for this contingency table, what are the expected
frequencies for the first row, rounded to two decimal places?
72. For a chi-square test of homogeneity for this contingency table, what are the observed
frequencies for the second column?
73. For a chi-square test of homogeneity for this contingency table, what are the expected
frequencies for the second column, rounded to two decimal places?
74. To perform a chi-square test of homogeneity for this contingency table at the 10%
significance level, what is the critical value of chi-square?
A) 5.991 B) 4.605 C) 3.841 D) 2.706
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Page 15
75. To perform a chi-square test of homogeneity for this contingency table, what is the value
of the chi-square test statistic (rounded to three decimal places)?
Use the following to answer questions 76-77:
A random sample of 25 elements selected from a population produced a variance equal to 3.937.
Assume that the population is normally distributed.
76. Based on this sample, the 95% confidence interval for the population variance, rounded
to three decimal places, is:
77. Based on this sample, the 95% confidence interval for the population standard deviation,
rounded to three decimal places, is:
Use the following to answer questions 78-79:
A random sample of 16 elements selected from a population produced a variance equal to 7.954.
Assume that the population is normally distributed.
78. Based on this sample, the 99% confidence interval for the population variance, rounded
to three decimal places, is:
79. Based on this sample, the 99% confidence interval for the population standard deviation,
rounded to three decimal places, is:
Chapter 11
Page 16
Use the following to answer questions 80-81:
A random sample of 20 elements selected from a population produced a variance equal to
11.072. Assume that the population is normally distributed.
80. Based on this sample, the 90% confidence interval for the population variance, rounded
to three decimal places, is:
81. Based on this sample, the 90% confidence interval for the population standard deviation,
rounded to three decimal places, is:
Use the following to answer questions 82-83:
A random sample of 29 workers selected from a large company produced a variance of their
weekly earnings equal to 8124. Assume that the population is normally distributed.
82. Based on this sample, the 95% confidence interval for the variance of the weekly
earnings of all of this company’s employees, rounded to three decimal places, is:
83. Based on this sample, the 95% confidence interval for the standard deviation of the
weekly earnings of all of this company’s employees, rounded to the nearest cent, is:
Use the following to answer questions 84-85:
A random sample of 25 elements selected from a population produced a variance equal to 4.959.
The null hypothesis is that the population variance is less than or equal to 3.90 and the alternative
hypothesis is that the population variance is greater than 3.90. Assume that the population is
normally distributed. The significance level is 1%.
Chapter 11
84. The critical value of chi-square is:
A) 42.980 B) 45.559 C) 41.638 D) 44.181
85. The value of the chi-square test statistic is, rounded to three decimal places:
Use the following to answer questions 86-87:
A random sample of 20 elements selected from a population produced a variance equal to 9.606.
The null hypothesis is that the population variance is equal to 10.05 and the alternative
hypothesis is that the population variance is not equal to 10.05. Assume that the population is
normally distributed. The significance level is 5%.
86. The critical values of chi-square are:
A) 10.117 and 30.144 C) 7.633 and 36.191
B) 8.231 and 31.526 D) 8.907 and 32.852
87. The value of the chi-square test statistic is, rounded to three decimal places:
Use the following to answer questions 88-89:
A random sample of 28 elements selected from a population produced a variance equal to
16.682. The null hypothesis is that the population variance is greater than or equal to 18.70 and
the alternative hypothesis is that the population variance is less than 18.70. Assume that the
population is normally distributed. The significance level is 2.5%.
88. The critical value of chi-square is:
A) 14.573 B) 43.195 C) 41.923 D) 13.844
89. The value of the chi-square test statistic is, rounded to three decimal places:
Chapter 11
Use the following to answer questions 90-91:
The variance of the prices of all college textbooks was 81.30 last year. A recent sample of 20
college textbooks produced a variance of their prices equal to 164.649. The null hypothesis is
that the current variance of the prices of all college textbooks is equal to 81.30 and the alternative
hypothesis is that the current variance of the prices of all college textbooks is greater than 81.30.
Assume that the prices of college textbooks are normally distributed. The significance level is
1%.
90. The critical value of chi-square is:
A) 36.191 B) 38.582 C) 39.997 D) 37.566
91. The value of the chi-square test statistic is, rounded to three decimal places:
Use the following to answer questions 92-93:
A researcher claims that the variance of the heights of all female college basketball players is
4.80 square inches. A random sample of 28 female college basketball players produced a
variance of their heights equal to 11.122 square inches. The null hypothesis is that the variance
of the heights of all female college basketball players is equal to 4.80 square inches and the
alternative hypothesis is that the variance of the heights of all female college basketball players
is not equal to 4.80. Assume that the population is normally distributed. The significance level is
5%.
92. The critical values of chi-square are:
A) 13.844 and 41.923 C) 15.308 and 44.461
B) 14.573 and 43.195 D) 12.879 and 40.113
93. The value of the chi-square test statistic is, rounded to three decimal places:
Chapter 11
94. Jean, an expert on dental hygiene, hypothesizes that the dental hygiene of students at the
Westwood Elementary School is similar to that of students at Easton Elementary. In order
to test her hypothesis, she collects information about children at each school from dentists
in the area, recording the number of cavities that each child has had in the past year. Her
findings appear in the following table.
Tooth Decay Level
Westwood School
Easton School
No Cavities
10
9
One Cavity
8
12
Two Cavities
14
6
Three or more
Cavities
6
8
The null hypothesis is that the proportions of students with no cavities, one cavity, two
cavities, and three or more cavities are relatively the same between schools. What is the
value of the test statistic, rounded to three decimal places, that Jean will use?
95. Using the table for the chi-square distributions, find the lower 10% point when d.f. = 17.
96. Find the probability of
236.42
when d.f. = 24.
97. Find the probability of
21.73
when d.f. = 9.
A) 0.005 B) 0.1 C) 0.01 D) 0.025
98. Find the probability of
2
7.63 32.85
when d.f. = 19.