Question

1. For a sample of 400 correctional officers at Lucasville State Prison, a researcher believes there is a

relationship between “years on the job” and “willingness to help raise money for adult charities.” Using

the following data, test the null hypothesis at the .05 level of significance that willingness to help raise

donations does not differ by length of service as a correctional officer. In so doing, identify: (1) the

research and null hypothesis, (2) the critical value needed to reject the null, (3) the decision that you made

upon analyzing the data, and (4) the conclusion you have drawn based on the decision you have made.

*Please show all work*

Years as a Correctional Officer

Willingness to Help	One	Two	Three	Four or More	Total
Willing	60	64	60	60	244
Unwilling	60	56	20	20	156
	120	120	80	80	400

Answer 1

Ans:

Chi square test for independence:

H₀:There is no association between “years on the job” and “willingness to help raise money for adult charities.”

Ha:There is association between “years on the job” and “willingness to help raise money for adult charities.”

degree of freedom=(2-1)*(4-1)=3

critical chi square value=CHIINV(0.05,3)=7.815

Expected count=row sum*column sum/overall sum

	Observed(fo)
	One	Two	Three	Four or more	Total
Willing	60	64	60	60	244
Unwilling	60	56	20	20	156
Total	120	120	80	80	400
	Expected(fe)
	One	Two	Three	Four or more	Total
Willing	73.20	73.20	48.80	48.80	244
Unwilling	46.80	46.80	31.20	31.20	156
Total	120	120	80	80	400
	Chi square=(fo-fe)^2/fe
	Perfect	Made 4 U	25 Hours		Total
Rejected	2.380	1.156	2.570	2.570	8.678
Perfect	3.723	1.809	4.021	4.021	13.573
Total	6.103	2.965	6.591	6.591	22.250

Test statistic:

Chi square=22.250

As,test statistic is greater than critical chi square value of 7.815,so we reject the null hypothesis.

There is sufficient evidence to conclude that “years on the job” and “willingness to help raise money for adult charities” are associated.