Question

A rural county hospital offers several health services. The hospital administrators conducted a poll to determine whether the residents’ satisfaction with the available services depends on their gender. A random sample of 1000 adult county residents was selected. The gender of each respondent was recorded and each was asked whether he or she was satisfied with the services offered by the hospital. The resulting data are shown in the table below. Using a significance level of 0.05, conduct an appropriate test to determine if, for adult residents of this county, there is an association between gender and whether or not they were satisfied with services offered by the hospital.

	Male	Female
Satisfied	382	418
Not Satisfied	80	120

Answer 1

The null and alternate hypothesis are:

H0: There is no association between gender and whether or not they were satisfied with services offered by the hospital.
Ha: There is an association between gender and whether or not they were satisfied with services offered by the hospital.

Observed frequencies(Oi):

	Male	Female	TOTAL
Satisfied	382	418	800
Not Satisfied	80	120	200
	462	538	1000

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

Expected frequencies(Ei):

	Male	Female	TOTAL
Satisfied		430.4	800
Not Satisfied	92.4	107.6	200
	462	538	1000

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 there is an association between gender and whether or not they were satisfied with services offered by the hospital.