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.

	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

Minitab Printout of GPA Based on Gender and Class
Analysis of Variance for GPA
Source	DF	SS	MS	F	P
Gender	1	0.281	0.281	1.26	0.273
Class	3	2.226	0.742	3.32	0.037
Interaction	3	0.286	0.095	0.43	0.736
Error	24	5.365	0.224
Total	31	8.159

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

class, with four levels

GPA, with three levels

GPA, with four levels

gender, with two levels

class, with five levels

income, 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 0.01.

F	=
P-value	=

At the 1% level of significance, ---Select one--- reject/do not reject H₀.
The data ---Select one--- do not indicate any interaction/indicate an 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 ? = 0.01. (Enter NONE in any unused answer blanks.)

F	=
P-value	=

At the 1% level of significance, ---Select one--- 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 ? = 0.01. (Enter NONE in any unused answer blanks.)

F	=
P-value	=

At the 1% level of significance, ---Select one--- do not reject/reject NONE H₀.

Answer 1

SolutionA:

class, with four levels they are:

class (freshman, sophomore, junior, senior)

gender, with two levels

males and females

GPA, 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 0.01.

F for interaction

F=0.43

p=0.736

alpha=1%=0.01

p>alpha

Do not reject Ho.

no interaction

do not indicate any interaction between factors.

Solutionc:

For class

F=3.32

p=0.037

alpha=1%=0.01

p>alpha

Do not reject H0.

There is no difference in mean GPA based on class.

Solutiond:

F=1.26

p=0.273

alpha=1%=0.01

p>alpha

Do not reject Ho

there is no difference in mean GPA based on gender.