Question

1. The General Social Survey (2008) asked a random sample of people whether they agree with the following statement: A husband’s job is to earn money; a wife’s job is to take care of the home. Based on this data (displayed below), conduct a chi-square hypothesis test to assess whether there are statistically significant gender differences in feelings about gender roles ( = 0.05).

	Male	Female	Total
Agree	181	195	376
Neither	142	145	287
Disagree	290	413	703
Total	613	753	1,366

a. Write out the hypotheses

b. Calculate degrees of freedom .

c. Construct a table of expected frequencies (fe).

d. Compute the chi-square statistic. Create a table like the ones we used in class to help you.

e. Determine the p-value using the appropriate Appendix.

Answer 1

a.

Null Hypothesis(H0):

Gender and feelings about gender roles are independent, i.e., there are statistically no significant gender differences in feelings about gender roles.

Alternative Hypothesis(H1):

Gender and feelings about gender roles are not independent, i.e., there are statistically significant gender differences in feelings about gender roles.

b.

No. of columns, c =2 (Male, Female)

No. of rows, r =3 (Agree, Neither, Disagree)

Degrees of freedom, df =(c-1)(r-1) =(2-1)(3-1) =2

c.

Table of expected frequencies (fe):

Formula: fe =(corresponding row total*corresponding column total)/Overall total

	Male	Female	Total
Agree	(376*613)/1366 =169	(376*753)/1366 =207	376
Neither	129	158	287
Disagree	315	388	703
Total	613	753	1366

d.

Computation of the chi-square statistic:

Observed frequencies: fo	Expected frequencies: fe	(fo - fe)2/fe
181	169	0.8521
142	129	1.3101
290	315	1.9841
195	207	0.6957
145	158	1.0696
413	388	1.6108
=1366	=1366	=7.5224

Chi-square statistic, =7.5224

e.

For the test statistic, =7.5224 at df =2, the p-value =0.0233

Conclusion:

Since p-value: 0.0233 < 0.05 significance level, we reject the null hypothesis(H0) at 5% significance level.

Thus, we have a sufficient evidence to claim that there are statistically significant gender differences in feelings about gender roles.