Question

q4

Source Of Variation Treatments Sum Degrees Of Freedom Mean Of Squares Square Error 28,67 Total 946 c) If it is necessary, determine subgroups by applying a post-hoc comparison, according to your decision in part b). Q-4 (25 points): A sample of 1545 men and an independent sample of 1691 women were used to compare amount of housework done by women and men dual-earner marriages. The study showed that 67,5% of the men felt the division of housework was fair and 60,8% of the women felt the division of housework was fair (American Journal of Sociology, September, 1994). Is the proportion of men who felt the division of housework was fair greater than the proportion of women who felt the division of housework was fair? Support your conclusion with a statistical test using a 0.05 level of significance. GOOD LUCK!

Answer 1

Solution:

Let p1 be the proportion of men who felt the division of housework was fair and p2 be the proportion of women who felt the division of housework was fair.

The null and alternative hypotheses are:

Ho: P1 = P2

Ha: P1 > P2

Under the null hypothesis, the test statistic:

P1 – P2 VĐp(1 – Pp) (+ :)

Where:

P1 = 0.675, P2 = 0.608

(0.675 x 1545) + (0.608 x 1691) y = 0.6400 1545 + 1691

0.675 - 0.608 0.64(1 - 0.64) (1ਖੇਡ + )

=3,966

The p-value is:

p - value = P(Z > 3.966) = 0.0000

Conclusion: Since the p-value is less than the significance level 0.05, we, therefore, reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the proportion of men who felt the division of housework was fair is greater than the proportion of women who felt the division of housework was fair.