Question

Chapter 7, Section 2, Exercise 033 Find the expected count and the contribution to the chi-square statistic for the (Control, Agree) cell in the two-way table below. Strongly Agree Agree Neutral Disagree Strongly Disagree Control 36 47 6 12 11 Treatment 56 45 12 7 2 Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places. Expected count = contribution to the chi-square statistic =

Answer 1

H0: There is no relationship between Control and Agree statistics

H1: There is relationship between Control and Agree statistics

Let the los be alpha = 5%

The observed frequencies are

	Strong Agree	Agree	Nautral	Disagree	Strong Disagree	Total
Control	36	47	6	12	11	112
Women	56	45	12	7	2	122
Marginal Total	92	92	18	19	13	234

The expected frequencies are

	Strong Agree	Agree	Nautral	Disagree	Strong Disagree	Total
Control	44.034	44.034	8.615	9.094	6.222	112
Women	47.966	47.966	9.385	9.906	6.778	122
Total	92	92	18	19	13	234

The Chisquare contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
36	44.034	1.466
47	44.034	0.2
6	8.615	0.794
12	9.094	0.929
11	6.222	3.669
56	47.966	1.346
45	47.966	0.183
12	9.385	0.729
7	9.906	0.852
2	6.778	3.368
	Total:	13.536

Degrees of freedom: 4

Test Statistic, X^2: 13.536
Critical X^2: 9.48772
P-Value: 0.0089

Here Chi-square value > Chi-square critical value and P-value < alpha 0.05 so we reject H0

Thus we conclude that there is relationship between Control and Agree statistics