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 *H*_{0}.

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 *H*_{0}.

(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 *H*_{0}.

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.

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