Does college grade point average (GPA) depend on gender? Does it depend on class

Question

Does college grade point average (GPA) depend on gender? Does it depend on class (freshman, sophomore, junior, senior)? In a study, the following GPA data were obtained for random samples of college students in each of the cells.

(a) List the factors and the number of levels of each factor. (Select all that apply.)

class, with five levelsincome, with four levelsGPA, with three levelsgender, with two levelsGPA, with four levelsclass, with four levels

(b) Use two-way ANOVA and the Minitab printout to determine if there is any evidence of interaction between the two factors at a level of significance of 0.1.

At the 10% level of significance,  ---Select--- reject do not reject H0.
The data  ---Select--- indicate an interaction do not indicate any interaction between factors.

(c) If there is no evidence of interaction, use two-way ANOVA and the Minitab printout to determine if there is a difference in mean GPA based on class. Use ? = 0.1. (Enter NONE in any unused answer blanks.)

At the 10% level of significance,  ---Select--- do not reject reject NONE H0.

(d) If there is no evidence of interaction, use two-way ANOVA and the Minitab printout to determine if there is a difference in mean GPA based on gender. Use ? = 0.1. (Enter NONE in any unused answer blanks.)

At the 10% level of significance,  ---Select--- do not reject reject NONE H0.

Class Gender Freshman Sophomore Junior Senior Male 2.8    2.1
2.7    3.0 2.5    2.3
2.9    3.5 3.1    2.9
3.2    3.8 3.8    3.6
3.5    3.1 Female 2.3    2.9
3.5    3.9 2.6    2.4
3.3    3.6 2.6    3.6
3.3    3.7 3.2    3.5
3.8    3.6

Explanation / Answer

a)

gender -2 levels

class- 4levels

b)

F =0.43

p value =0.736

At the 10% level of significance do not reject H0

The data do not indicate any interaction between factors.

c)

F =3.32

p value =0.037

At the 10% level of significance reject H0

d)

F =1.26

p value =0.273

At the 10% level of significance do not reject H0

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