Deck 11: Tables

Question 1

An F-test can be used to compare the variances of three or more means.

Answer 1

False

Question 2

When finding the degrees of freedom for the F-distribution, d. f. N is equal to one less than the number of
groups.

Answer 2

False

Question 3

For a disordinal interaction, the main effects can be interpreted independently of each other.

Answer 3

False

Question 4

If one tested at the 1% level of significance, one would declare that averaging over the 3 diets, weight
gains were significantly different between males and females (i.e., that the main effect of gender is
significant).

Question 5

If there are 3 means to be compared, how many different comparisons are possible?

A) 2
B) 3
C) 5
D) 6

Question 6

If the means of four different groups were compared at , and the critical value of the F-test was 3.96, the critical value for the Scheffé test would be 15.84.

Question 7

In a two-way ANOVA procedure, variable A has four levels and variable B has two levels. The d.f.N. for
factor would be 3.

Question 8

Which of the following assumptions is not made for the F-test for comparing three or more means?

A) The populations from which the samples were obtained must be normally distributed.
B) The samples must be independent of each other.
C) The sample sizes must be equal.
D) The variances of the populations must be equal.

Question 9

Question 10

For three groups, the F-test can show whether or not a difference exists among three or more means and
where the difference lies.

Question 11

To find the critical value for the Tukey test, the number of means, k, and the degrees of freedom
associated with the between-group variance, n, are needed.

Question 12

The value of the F-distribution can be negative.

Question 13

When performing an F-test, if the means differ significantly, the between-group variance will be much
smaller than the within-group variance.

Question 14

A researcher can use the Scheffé or the Tukey test to determine where the difference in the means lies
once the null hypothesis for the F-test has been rejected.

Question 15

The ANOVA technique is an abbreviation for the following term:

A) analysis of variance
B) variance
C) Scheffé test
D) Tukey test

Question 16

When the absolute value of q is less than the critical value for the Tukey test, there is a significant
difference between the two means being compared.

Question 17

To compare 7 means, which of the following techniques would be applicable?

A) Analysis of Variance
B) ANOVA
C) Both (A) and (B)
D) Neither (A) nor (B)

Question 18

If a researcher wanted to use the t-test to compare 10 means, two at a time, 45 tests would need to be
performed.

Question 19

The F-test for comparing means is always right-tailed.

Question 20

In order to conduct the Scheffé test, one must compare the means two at a time, using all possible
combinations of means.

Question 21

Assuming that there is a significant difference between the means of the three coffee machines, what would the critical value be for the Tukey test at ?

A) 3.70
B) 3.08
C) 3.77
D) 3.73

Question 22

A researcher is comparing three groups of the same size. The sample mean of the first group is 12, the sample mean of the second group is 14, and the sample mean of the third group is 16. If the Tukey q-test
Value for comparing group 1 with group 2 is 2.6, then the Tukey q-test value for comparing group 2 with
Group 3 will be:

A) 2.6
B) 5.2
C) 10.4
D) Cannot be determined with the information given

Question 23

A researcher is comparing 3 groups to test if they have the same means. There are 51 data values altogether. The degrees of freedom for the Between (dfB) and the degrees of freedom for the Within
(dfW) are:

A) dfB = 48, dfW = 50
B) dfB = 2, dfW = 48
C) dfB = 2, dfW = 50
D) dfB = 3, dfW = 50

Question 24

A researcher is comparing three groups of the same size. The sample mean of the first group is 12, the sample mean of the second group is 16, and the sample mean of the third group is 20. If the Scheffé F-test
Value for comparing group 1 with group 2 is 7.4, then the Scheffé F-test value for comparing group 2 with
Group 3 will be:

A) 3.7
B) 7.4
C) 14.8
D) Cannot be determined with the information given

Question 25

What is the between-group variance for the three coffee machines?

A) 0.017
B) 0.098
C) 0.057
D) 0.086

Question 26

If a researcher wanted to compare the F-value with the critical value for F at , what would that critical F be?

A) 3.70
B) 3.08
C) 3.89
D) 3.73

Question 27

What is the grand mean for the data given above?

A) 12.08
B) 11.96
C) 11.82
D) 11.85

Question 28

A) -0.01
B) -0.29
C) -1.51
D) -4.00

Question 29

Is there a significant difference between the means for vending machines A, B, and C?

A) Yes, there is a significant difference between the means.
B) No, there is no significant difference between the means.
C) The F-test cannot be used to answer whether or not there is a significant difference between the means.
D)The Scheffé test needs to be performed in order to determine whether or not there is a significant difference between the means.

Question 30

Complete the formula for the Tukey test: $q =$

A)


B)
$\frac{n 1 s_{i}^{2}}{n 1}$

C) $\frac { \bar { X } _ { i } \bar { X } _ { f } { } ^ { 2 } } { s _ { w } ^ { 2 } 1 / n - 1 / n _ { j } }$

D) $\frac { \bar { X } _ { t } - \bar { X } _ { f } } { \sqrt { s _ { w } ^ { 2 } } / n }$

Question 31

What would the Tukey test value be for comparing the means of machine B and machine C at ?

A) -1.61
B) -1.17
C) -7.72
D) -4.46

Question 32

What is the F-value for the coffee machines?

A) 2.25
B) 5.06
C) 6.62
D) 4.86

Question 33

What is the within-group variance for the three coffee machines?

A) 0.017
B) 0.0136
C) 0.13
D) 0.029

Question 34

Question 35

Question 36

Question 37

The between-group variance and the error variance are sometimes referred to as:

A) ANOVA summary table
B) mean squares
C) main effects
D) interaction effects

Question 38

A) F = 0.91
B) F = 1.28
C) F = 2.01
D) F = 2.74

Question 39

A) 0.15
B) 0.47
C) 6.59
D) 2.13

Question 40

Question 41

A researcher is comparing three groups of the same size. The sample mean of the first group is 14, the sample mean of the second group is 17, and the sample mean of the third group is 20. If the Scheffé F-test
Value for comparing group 1 with group 2 is 5.4, then the Scheffé F-test value for comparing group 1 with
Group 3 will be:

A) 5.4
B) 10.8
C) 21.6
D) Cannot be determined with the information given

Question 42

The head of the English department wants to determine if the average number of students taking
an English course differs depending upon the time of day that the course is being offered.

Given the between-group variance (determined in the previous question) and the fact that the F-test value is 6.00, what is the within-group variance for the three class times?

A) 23.40
B) 46.80
C) 3.90
D) 7.18

Question 43

A researcher is comparing three groups of the same size. The sample mean of the first group is 11, the sample mean of the second group is 13, and the sample mean of the third group is 15. If the Tukey q-test
Value for comparing group 1 with group 2 is -2.1, then the Tukey q-test value for comparing group 1 with
Group 3 will be:

A) -2.1
B) -4.2
C) -8.4
D) Cannot be determined with the information given

Question 44

The head of the English department wants to determine if the average number of students taking
an English course differs depending upon the time of day that the course is being offered.

What is the between-group variance for the data given above.

A) 23.40
B) 46.80
C) 3.90
D) 7.18

Question 45

A) Only the null hypothesis concerning Factor A should be rejected
B) Only the null hypothesis concerning Factor B should be rejected
C) Only the null hypothesis concerning Factor A and the Interaction (AxB) effect should be rejected
D) All of the null hypotheses should be accepted

Question 46

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected; in other words, the 7 population means (from samples of the same size) are not all equal. We should expect that:

Question 47

A) Only the null hypothesis concerning Factor A should be rejected
B) Only the null hypothesis concerning Factor B should be rejected
C) Only the null hypothesis concerning Factor A and the Interaction (AxB) effect should be rejected
D) All of the null hypotheses should be accepted

Question 48

A) disordinal interaction
B) ordinal interaction
C) polar interaction
D) cardinal interaction

Question 49

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected; in other words, the 4 population means are not all equal. We should expect that:

Question 50

A) The null hypothesis concerning Factor A should be rejected
B) The null hypothesis concerning Factor B should be rejected
C) The null hypothesis concerning Factor A and the Interaction (AxB) effect should be rejected
D) All of the null hypotheses should be accepted

Question 51

A researcher is performing a two-way ANOVA using two factors. The first factor has 4 levels and the second factor has 10 levels. In the ANOVA Summary Table, the degrees of freedom for the interaction
Between the first and second factors will be:

A) 27
B) 30
C) 36
D) 40

Question 52

An experiment has been designed to study the effectiveness of a new diet on weight gain for use with
anorexic individuals. The diet is available in both a solid and a liquid form.
The two new diets and a standard control diet were randomly assigned to 15 women and 15 men. Thus,
each of the 3 diets was assigned to 5 men and 5 women. The weight gains attained after 12 weeks were
recorded for each of the participants and the corresponding averages are summarized in the following
B B'
The degrees of freedom for error are:

A) 14
B) 24
C) 29
D) 30

Question 53

A) The null hypothesis concerning Factor A should be rejected
B) The null hypothesis concerning Factor B should be rejected
C) The null hypothesis concerning Factor A and the Interaction (AxB) effect should be rejected
D) All of the null hypotheses should be accepted

Question 54

If the figure below is the result of a two-way ANOVA, which of the following statements would apply?

A) There is no significant interaction effect.
B) There is a significant interaction effect.
C) The main effects should not be interpreted without considering the interaction effect.
D) The graph does not give any indication of whether or not there is an interaction effect.

Question 55

Is there a significant difference between the mean attendance for the classes given ?

A) Yes, there is a significant difference between the means.
B) No, there is no significant difference between the means.
C) The F-test cannot be used to answer whether or not there is a significant difference between the means.
D)The Scheffé test needs to be performed in order to find whether or not there is a significant difference between the means.

Question 56

Which of the following assumptions does not apply to the two-way ANOVA?

A) The populations from which the samples are obtained must be normally or approximately normally distributed.
B) The samples must be independent of each other.
C) The means of the populations must be equal.
D) The groups must be equal in sample size.

Question 57

An experiment has been designed to study the effectiveness of a new diet on weight gain for use with
anorexic individuals. The diet is available in both a solid and a liquid form.
The two new diets and a standard control diet were randomly assigned to 15 women and 15 men. Thus,
each of the 3 diets was assigned to 5 men and 5 women. The weight gains attained after 12 weeks were
recorded for each of the participants and the corresponding averages are summarized in the following
B B'
The degrees of freedom for the interaction between diet and gender are:

A) 1
B) 2
C) 3
D) 4

Question 58

A) disordinal interaction
B) ordinal interaction
C) There is no interaction because the lines do not cross.
D) cardinal interaction

Question 59

The total number of degrees of freedom for a two-way ANOVA is equal to one less than the total number
of samples.

Question 60

A researcher is performing a two-way ANOVA using two factors. The first factor has 4 levels and the second factor also has 4 levels. In the ANOVA Summary Table, the degrees of freedom for the first and
Second factors will be:

A) 4 d.f. for the first factor and 4 d.f. for the second factor
B) 3 d.f. for the first factor and 3 d.f. for the second factor
C) 5 d.f. for the first factor and 5 d.f. for the second factor
D) 16 d.f. for the first factor and 16 d.f. for the second factor

Question 61

This experiment is best described as a(n):

A) randomized survey.
B) completely randomized design.
C) factorial treatment design carried out in a completely randomized experimental design.
D) observational study.

Question 62

The ________________ variance is made by computing the variance using all the data and is not affected
by differences in the means.
________________________________________

Question 63

Question 64

When there is one independent variable, the analysis of variance is called a __________ ANOVA.
________________________________________

Question 65

Question 66

In a two-way ANOVA design, variable A has four levels and variable B has two levels. There are eight
data values in each cell. What is the d.f.N. for factor B?

Question 67

The ______________ test can be used even if the sample sizes are not equal.
________________________________________

Question 68

Qualitative independent variables can also be called ______________.
________________________________________

Question 69

The ____________ test can be used after the analysis of variance has been completed to make pairwise
comparisons between means when groups have the same sample size.
________________________________________

Question 70

If there is no difference in the means, the _____________ variance will be approximately equal to the
within-group variance.
________________________________________

Question 71

Each independent variable investigated could have two or more different treatments or
______________.
________________________________________
e