Question

Chi-Square Test for Independence

Using Chi-Square, we are looking to see if there is a significant difference between what we would expect results to be, and what the actual results were. That is, expected vs. observed.   Use alpha = .05

Listed below are data from a survey conducted recently where Males and Females responded to their happiness with their supervisor (this is fictitious data).

Response	Male	Female	Total
Not at all	23	25	48
Somewhat	13	22	35
Very	26	16	42
Total	62	63	125

What is your null hypothesis?

What is your alternative hypothesis?

What is the Chi-Square value?

Is there significance evidence that a difference exists between the actual males and female responses in this sample and the expected male/female responses in the population? YES OR NO

Answer 1

The following cross-tabulation have been provided. The row and column total have been calculated and they are shown below:

	Male	Female	Total
NotAtAll	23	25	48
Somewhat	13	22	35
Very	26	16	42
Total	62	63	125

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0​: The two variables - response and gender are independent

Ha​: The two variables - response and gender are dependent

This corresponds to a Chi-Square test of independence.

Test Statistics

The Chi-Squared statistic is computed as follows:

Based on the information provided, the significance level is α=0.05 , the number of degrees of freedom is df=(3−1)×(2−1)=2, so then the rejection region for this test is R={χ2:χ2>5.991}.

Since it is observed that , it is then concluded that the null hypothesis is not rejected. Therefore, there is NOT enough evidence to claim that the two variables are dependent, at the 0.05 significance level.

NO, there is not significance evidence that a difference exists between the actual males and female responses in this sample and the expected male/female responses in the population.

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