1. To use an F distribution, the random variable must be:
A) a discrete random variable
B) a continuous random variable
C) a qualitative random variable
D) either a discrete or a continuous random variable
2. The shape of the F distribution curve is:
A) skewed to the left B) skewed to the right C) symmetric D) rectangular
3. Which of the following is not a characteristic of an F distribution?
A) The F distribution is continuous and skewed to the right.
B) The F distribution has two numbers of degrees of freedom: degrees of freedom
for the numerator and for the denominator.
C) The F distribution has two parameters: the mean and the standard deviation.
D) The units of an F distribution are always nonnegative.
4. The units of an F distribution:
A) are always negative C) are always nonnegative
B) are always positive D) can be negative, zero, or positive
5. The parameters of the F distribution are:
A) the mean and the standard deviation
B) the sample size minus one and F
C) the degrees of freedom for the numerator and the degrees of freedom for the
denominator
D) F and n, where n is the sample size
6. The F value for 9 degrees of freedom for the numerator, 12 degrees of freedom for the
denominator, and a .01 area in the right tail is:
A) 2.80 B) 5.11 C) 4.74 D) 4.39
Chapter 12
7. The F value for 25 degrees of freedom for the numerator, 14 degrees of freedom for the
denominator, and a .05 area in the right tail is:
A) 2.78 B) 2.34 C) 3.19 D) 1.87
8. We can use the analysis of variance procedure to test hypotheses about:
A) the mean of one population C) two or more population proportions
B) the proportion of one population D) two or more population means
9. Which of the following assumptions is not required to use ANOVA?
A) The populations from which the samples are drawn are (approximately) normally
distributed.
B) The populations from which the samples are drawn have the same variance.
C) All samples are of the same size.
D) The samples drawn from different populations are random and independent.
10. In a one-way ANOVA, we analyze only one:
A) mean B) population C) sample D) variable
11. A one-way ANOVA test:
A) is a left-tailed test
B) is a right-tailed test
C) is a two-tailed test
D) can be a two-tailed, a right-tailed, or a left-tailed test
12. To make tests of hypotheses about more than two population means, we use the:
A) t distribution C) chi-square distribution
B) normal distribution D) analysis of variance procedure
Chapter 12
Use the following to answer questions 13-22:
The table shown below gives information on a variable for three samples selected from three
normally distributed populations with equal variances.
Sample I
Sample II
Sample III
15
14
21
15
9
16
28
18
24
19
10
13
12
19
19
By using ANOVA, we wish to test the null hypothesis that the means of the three corresponding
populations are equal. The significance level is 1%.
13. The value of
x
is:
14. The value of
2
x
is:
15. The value of SSB, rounded to two decimal places, is:
16. The value of SSW is:
17. The value of MSB is:
18. The value of MSW, rounded to three decimal places, is:
Chapter 12
19. The degrees of freedom for the numerator of the F distribution are:
20. The degrees of freedom for the denominator of the F distribution are:
21. The critical value of F is:
A) 4.81 B) 2.76 C) 6.93 D) 99.42
22. The value of the test statistic F, rounded to three decimal places, is:
Use the following to answer questions 23-32:
The table shown below gives information on a variable for four samples selected from four
normally distributed populations with equal variances.
Sample I
Sample II
Sample III
Sample IV
5
8
19
16
7
14
11
12
11
20
8
19
9
20
11
8
6
13
4
7
13
16
By using ANOVA, we wish to test the null hypothesis that the means of the four corresponding
populations are equal. The significance level is 5%.
23. The value of
x
is:
Chapter 12
24. The value of
2
x
is:
25. The value of SSB, rounded to three decimal places, is:
26. The value of SSW is:
27. The value of MSB, rounded to three decimal places, is:
28. The value of MSW, rounded to three decimal places, is:
29. The degrees of freedom for the numerator of the F distribution are:
30. The degrees of freedom for the denominator of the F distribution are:
31. The critical value of F is:
A) 5.48 B) 3.16 C) 7.15 D) 1.84
32. The value of the test statistic F, rounded to three decimal places, is:
Chapter 12
Use the following to answer questions 33-42:
A dietician wanted to test three different diets to find out whether or not the mean weight loss for
each of these diets is the same. Fifteen overweight persons were selected at random, then
randomly divided into three groups of five, and each group was assigned one of the diets. The
table shown below contains the weight loss information for these people after being on their
respective diets for six weeks.
Diet A
Diet B
Diet C
7
4
15
8
3
12
6
6
17
6
4
15
8
7
11
By using ANOVA, we wish to test the null hypothesis that the mean weight loss is the same for
the three diets. The significance level is 2.5%.
33. The value of
x
is:
34. The value of
2
x
is:
35. The value of SSB is:
36. The value of SSW is:
37. The value of MSB is:
Chapter 12
38. The value of MSW, rounded to three decimal places, is:
39. The degrees of freedom for the numerator of the F distribution are:
40. The degrees of freedom for the denominator of the F distribution are:
41. The critical value of F is:
A) 4.75 B) 3.18 C) 5.10 D) 9.57
42. The value of the test statistic F, rounded to three decimal places, is:
43. Which of the following is not a characteristic of the F distribution?
A) It has two numbers of degrees of freedom: df for the numerator, and df for the
denominator, and these two numbers may or may not be equal to each other.
B) It is symmetric.
C) It is continuous.
D) All units are nonnegative.
Chapter 12
Use the following to answer questions 44-48:
A market research company randomly divides 12 stores from a large grocery chain into three
groups of four stores each in order to compare the effect on mean sales of three different types of
displays. The company uses display type 1 in four of the stores, display type 2 in four others, and
display type 3 in the remaining four stores. Then it records the amount of sales (in $1,000’s)
during a one month period at each of the twelve stores. The table shown below reports the sales
information.
Display
Type I
Display
Type II
Display
Type III
109
135
160
116
137
150
135
123
147
115
120
128
By using ANOVA, we wish to test the null hypothesis that the means of the three corresponding
populations are equal. The significance level is 1%.
44. The value of SSB is:
45. The value of SSW, rounded to two decimal places, is:
46. The degrees of freedom for the numerator of the F distribution are:
47. The degrees of freedom for the denominator of the F distribution are:
48. The value of the test statistic F, rounded to three decimal places, is:
Chapter 12
Use the following to answer questions 49-53:
The marketing manager for a software company is trying to decide whether to market her
company’s newest product by mail, on television, or through the Internet. She selects 20
communities in which to test-market the product, advertising through one of the three media in
each community. The following table shows the amount of sales, in hundreds of dollars, for each
community:
Mail
TV
Internet
6
9
16
8
12
11
10
8
10
7
14
8
9
4
9
5
7
14
4
12
Sales are normally distributed and the standard deviations are equal for all three methods of
advertising. You are to test the hypothesis that the means are the same for all three treatments
using the ANOVA method.
49. The value of SSB, rounded to four decimal places, is:
50. What is the variance within samples, rounded to four decimal places?
51. The degrees of freedom for the numerator of the F distribution are:
52. The degrees of freedom for the denominator of the F distribution are:
53. The value of the test statistic F, rounded to three decimal places, is:
Chapter 12
54. Using ANOVA, you test the hypothesis that the means of 3 treatments are the same. You
calculate the MSW as 16.6. The value of the test statistic F is 2.1. What is the between
samples sum of squares, rounded to two decimal places?
Use the following to answer questions 55-61:
Your associate just took a lunch break and gave you the following incomplete ANOVA table she
was trying to finish before noon. The null hypothesis for this test is
0 1 2 3 4 5
:H
= = = =
.
Source of
Variation
Degrees of
Freedom
Sum of
Squares
Mean
Square
F
Between
33.9
Within
68.3
Total
29
55. How many data points were used in this analysis?
56. How many degrees of freedom are there for the between groups variation?
57. How many degrees of freedom are there for the within groups variation?
58. What is the value of the total sum of squares? Round your answer to one decimal place.
59. What is the value of the mean square between groups? Round your answer to three
decimal places.
Chapter 12
60. What is the value of the mean square within groups? Round your answer to three decimal
places.
61. What is the value of the test statistic F? Round your answer to three decimal places.
62. Find the critical value of F for d.f = (7, 2) and the area in the right tail = 0.025.
A) 39.36 B) 99.36 C) 19.35 D) 1.96