Question

Compute chi square and make a determination about the null hypothesis.  

Expected Frequencies	Men	Women	Total
Agree	269.2	316.8	586.0
Disagree	233.8	275.2	509.0
Total	503.0	592.0	1095.0
Observed Frequencies	Men	Women	Total
Agree	242.0	344.0	586.0
Disagree	261.0	248.0	509.0
Total	503.0	592.0	1095.0
(Observed-Expected)2 / Expected	Men	Women	Total
Agree	2.8	2.3	585.0
Disagree	3.2	2.7	509.0
Total	503.0	592.0	1095.0

Answer 1

Solution :

To test variables Gender(male,female) and response(agree,disagree) are independent or not.

The hypothesis are,

Null hypothesis Ho : The variables gender and response are independent.

Vs

Alternative hypothesis Ha : The variables gender and response are not independent.

Given that ,

Observed Frequency	Expected Frequency	(O-E)^2/E
242	269.2	2.8
344	316.8	2.3
261	233.8	3.2
248	275.2	2.7

So by taking the sum of values in the last column, we get the value of chi-square test statistics.

Now using chi-square table with degrees of freedom (r-1)*(c-1) = (2-1)*(2-1) = 1                        (where r=rows and c=columns) and level of significance = 0.05 , we get critical value 3.84.

Decisiosn rule : Reject Ho ,if test statistics > critocal value otherwise fail to reject Ho.

So here as Test statistics(11) > critical value ,we reject Ho.

Conclusion : The variables gender and response are not independent.