Question

In a telephone survey of 800 registered voters, the data are cross classified both by gender of respondent and by respondent’s opinion on an environmental bond issue.

                                                                                Bond issue

                                                                                For                         Against

                                                Men                      450                         150

                                                Women               160                      40  

We want to know whether there is good evidence that one’s gender influences whether a person is for or against the bond issue. Use the chi-square test to answer this question. State the hypotheses, discuss conditions, perform calculations, and report your conclusions. (Please Type)     

Answer 1

Solution:

Given: We have to test whether there is good evidence that one’s gender influences whether a person is for or against the bond issue.

That is we have to test if Gender and Bond issue are independent or not.

Thus we use following steps:

Step 1) State H0 and H1:

H0: Gender and Bond issue are independent

Vs

H1: Gender and Bond issue are not independent.

Step 2) Find Chi-square test statistic:

Where

O_ij = Observed frequencies for i^th row and j^th column.

E_ij = Expected frequencies for i^th row and j^th column.

Where

Thus we need to make following table:

	Bond Issue
Gender	For	Against	Total
Men	450	150	R1 =600
Women	160	40	R2 =200
Total	C1 = 610	C2 =190	N = 800

Thus we need to make following table:

Oij	Eij	Oij^2/Eij
450	457.5	442.623
150	142.5	157.8947
160	152.5	167.8689
40	47.5	33.68421
N = 800

Thus

Step 3) Find Chi-square critical value:

df = (R-1)X(C-1) =(2-1)X(2-1) = 1X1 = 1

df = 1

level of significance = 0.05

Chi-square critical value = 3.841

Step 4) Decision Rule:
Reject H0, if Chi-square test statistic value > Chi-square critical value = 3.841, otherwise we fail to reject H0.

Since Chi-square test statistic value = < Chi-square critical value = 3.841,we fail to reject H0.

Step 5) Conclusion:

Gender and Bond issue are independent

That is there is no evidence that one’s gender influences whether a person is for or against the bond issue.