Question

A group of sociologists conducted an analysis of the gender gap in faculty salaries. Data consistently indicate how women faculty members earn less than their male counterparts. Differences have been attributed to individual difference, as well as employer and institutional discrimination. For their analysis the sociologists obtained salary data on 158 men and 148 women, randomly chosen, from a large public research university. Men were estimated to earn an average of $42,340 with a standard deviation of $9,639.19, while women earned $33,865.98 with standard deviation $8,298.82.

(a) Test at the 5% significance level whether the average wages for both genders are the same. Find also the P–value of this test.

(b) Test at the 5% significance level whether the average wages for women are lower than those for men. Find also the P–value of this test.

(c) With 95% confidence, how much higher are the wages of men than those of women? [Hint: Find a CI for the difference of means

Answer 1

Men: x1bar = 42340, s1 = 9639.19 , n1= 158
Women: x2bar = 33865.98, s1 = 8298.82 , n1= 148

SE = sqrt(9639.19^2/158 + 8298.82^2/148) = 1026.3546

a)
Test statistic,
z = (42340 - 33865.98)/1026.3546 = 8.2564

p-value = 0.0000
Reject the null hypothesis.
Sufficient evidence to conclude that there is difference in the wages

b)
Test statistic,
z = (33865.98 - 42340)/1026.3546 = -8.2564

p-value = 0.0000
Reject the null hypothesis.
Sufficient evidence to conclude that there is women has lower wages

c)
ME = 1.96*1026.3546 = 2011.6550

CI = (42340 - 33865.98 - 2011.6550, 42340 - 33865.98 + 2011.6550)
= (6462.37, 10485.68)