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# Chi Square test and ANOVA

In a class of 100 students, the grades by gender are shown below:
A B C D F Row Total
Men 7 14 28 14 7 70
Women 8 6 7 6 3 30
Column Total 15 20 35 20 10 100

Can you conclude at a 95% confidence that the grade is independent of gender?

An experiment was conducted to compare the effectiveness of three training programs, A, B, and C, in training assemblers of a piece of electronic equipment. Fifteen employees were randomly assigned, 5 each, to the three programs. After the completion of the courses, each person was required to assemble four pieces of equipment, and the average length of time required to complete the assembly was recorded. Owing to resignation from the company, only 4 employees completed the program A and only 3 completed the program B while all 5 employees completed the program C. The result is as follows:
Training Program Average Assembly Time In Minutes
A 59 64 57 62
B 52 58 54
C 58 65 71 63 64

Do the data provides sufficient evidence to indicate a difference in mean assembly times for people trained by the three programs at a 95% confidence level?

#### Solution Preview

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Statistical Problems Need Help
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In a class of 100 students, the grades by gender are shown below:
A B C D F Row Total
Men 7 14 28 14 7 70
Women 8 6 7 6 3 30
Column Total 15 20 35 20 10 100

Can you conclude at a 95% confidence that the grade is independent of gender?

The null hypothesis tested is
H0: There is no association between gender and grade
H1: There is association between gender and grade

The test Statistic used is
where O - the observed frequency and E expected frequency
Expected frequency of the ijth cell is calculated as Ri- ith Row total
Cj -jth Column total , ...

#### Solution Summary

Chi-square test for independence and ANOVA test for comparison of variance are included.

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