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.   State the rejection rule using the critical value approach. Let alpha = 0.05.

3.   Calculate the expected frequency for the cell “No Degree” and “International Region”

4.   If the Chi Square statistic is 2.176, what is your conclusion?

Answer 1

1)

Ho:  managers’ education level is independent of which region they are from

H1:  managers’ education level is dependent of which region they are from

2)

Level of Significance =   0.05
Number of Rows =   3
Number of Columns =   2
Degrees of Freedom=(#row - 1)(#column -1) =   2
  
Critical Value =   5.991   [ Excel function: =CHISQ.INV.RT(α,DF) ]  

reject Ho, if test stat >5.991

3)

Expected frequency of a cell = sum of row*sum of column / total sum = 170*140/960 = 24.7917

4)

since, test stat=2.176< 5.991 , do not reject Ho

Conclusion:  managers’ education level is independent of which region they are from