Question

The following table contains observed frequencies for a sample of 200.  

	Column Variable
Row Variable	A	B	C
P	20	45	50
Q	30	26	29

Test for independence of the row and column variables using  α = .05.  

Compute the value of the  Χ 2 test statistic (to 2 decimals).

Answer 1

The hypothesis to be tested here is:

H0: The row and the column variable are independent.

against the alternative hypothesis

H1: The ow and the column variable are not independent.

To test the independence of the row and the column variable we will use a chi-square test.

We have the following row and column totals:

	Column Variable
Row Variable	A	B	C	Total
P	20	45	50	115
Q	30	26	29	85
Total	50	71	79	200

The expected frequency in each cell is given as:

Thus we have the following table for expected frequencies:

	Column Variable
Row Variable	A	B	C	Total
P	28.75	40.825	45.425	115
Q	21.25	30.175	33.575	85
Total	50	71	79	200

The test statistic for the chi-square test is given as:

Putting the values we have:

The degrees of freedom is given by: where r is the number of rows and c is the number of columns. So here the degrees of freedom is .

The chi-square critical value at 0.05 level of significance and 2 degrees of freedom is 5.9915.

Since the calculated value of the test-statistic is more than the chi-square critical value so we have sufficient evidence to reject the null hypothesis. Thus we conclude that the row and the column variable are not independent.