Question

The following is a summary of data for 960 branch managers in the two major regions of a Canadian Bank:

Education Level	Domestic Region	International Region	TOTAL
No Degree	120	20	140
Bachelor’s Degree	420	100	520
Post-graduate Degree	250	50	300
TOTAL	790	170	960

1.   State the null and alternative hypotheses for a Chi Square test to determine if managers’ education level is dependent of which region they are from. (2 Points)

2.   State the rejection rule using the critical value approach. Let alpha = 0.05. (2 Points)  

3.   Calculate the expected frequency for the cell “No Degree” and “International Region” (2 Points)

4.   If the Chi Square statistic is 2.176, what is your conclusion? (2 Points)

Answer 1

Solution:

1. The null and alternative hypotheses are:

H0: The Manager's education level is independent of the region they are from.

Ha: The Manager's education level is dependent of the region they are from.

2. The rejection rule using the critical value approach is:

Reject the null hypothesis if the chi-square statistic is greater than 5.991

Reject H0, if

3. The expected frequency for the cell “No Degree” and “International Region” is:

4. If the chi-square statistic is 2.176, we, fail to reject the null hypothesis because the chi-square statistic does not fall in the rejection region and conclude that the Manager's education level is independent of the region they are from