Question

Are the events (customer is urban) and (customer is suburban) independent?

Suburban: Male (196) Female (298)

Urban : Male (192) Female (173)

Answer 1

The null and alternate hypothesis are:

H0: The two events are independent.

Ha: The two events are not independent.

Let the level of significance be 5%.

Observed (O):

	Male	Female	TOTAL
Suburban	196	298	494
Urban	192	173	365
TOTAL	388	471	859

Now, Expected frequency = [(Row total) x (Column total)] / Table total

Expected (E):

	Male	Female	TOTAL
Suburban	223.134	270.866	494
Urban	164.866	200.134	365
TOTAL	388	471	859

Test statistic value =

The critical value is given by:

Since the test statistic value is greater than the critical value, so we have sufficient evidence to reject null hypothesis H0. Thus, we can say that the two given variables are not independent.