# Two Way ANOVA & Chi square test for Independence

See attached file for the tables.

3-35. A research firm wants to compare the miles per gallon of unleaded regular, mid-grade, and super premium gasoline. Because of differences in the performance of different automobiles, seven different automobiles were selected and treated as blocks. Therefore, each brand of gasoline was tested with each type of automobile. The results of the trials, in miles per gallon, are shown in the following table. At the .05 significance level, is there a difference in the gasoline and automobiles?

Automobile Regular Mid-grade Super Premium

1 21 23 26

2 23 22 25

3 24 25 27

4 24 24 26

5 26 26 30

6 26 24 27

7 28 27 32

3-75. A sample of employees at a large chemical plant was asked to indicate a preference for one of three pension plans. The results are given in the following table. Does it seem that there is a relationship between the pension plan selected and the job classification of the employees? Use the .01 significance level.

PENSION PLAN

JOB CLASSIFICATION PLAN A PLAN B PLAN C

SUPERVISOR 10 13 29

CLERICAL 19 80 19

LABOR 81 57 22

Instruction for last question: In all exercises, include MegaStat, Excel, or MINITAB exhibits to support your calculations.

State the hypotheses, show how the degrees of freedom are calculated, find the critical value of chisquare

from Appendix E or from Excel's function =CHIINV(alpha, deg_freedom), and interpret the p-value.

Tell whether the conclusion is sensitive to the level of significance chosen, identify cells that contribute

the most to the chi-square test statistic, and check for small expected frequencies. If necessary, you can

calculate the p-value by using Excel's function =CHIDIST(test statistic,deg_freedom). Note: Exercises marked

* are harder or require optional material.

15.18 Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Research question: At α = .01, is the degree of certainty independent of credits earned?

Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total

0-9 12 8 3 23

10-59 8 4 10 22

60 or more 1 7 11 19

Col Total 21 19 24 64

https://brainmass.com/statistics/chi-squared-test/two-way-anova-chi-square-test-for-independence-345865

#### Solution Summary

The solution provides step by step method for the calculation of chi square test for independence and two factor anova. Formula for the calculation and Interpretations of the results are also included.