Question

A sociologist studied gender differences in the average number of hours worked per day among employees at a law firm (there are 42 men and 19 women employed at this firm). She obtained the following results: men work, on average, 52 hour per week and women work, on average, 56 hour per week. The standard deviation for men is 12 hours and the standard deviation for women is 9 hours. Test the null hypothesis of no difference in the average number of hours worked by men and women (test the null at the .01 α level).

Answer 1

Given

	Men	Women
sample size n	42	19
Mean	52 hour/week	56 hour/week
std dev	12 hours	9 hours

Hypothesis

H0 :

H1:

level of significance alpha = 0.01

Assumning poplation variances unknown and not equal

degrees of freedom df = = 45.63 = 45

criteria for rejection :- if | test statistic| is more than |critical value| (t0.005,45 = 2.690) then we reject H0 otherwise fail to reject H0.

test statistic t = = -1.44

Since |test statistic| (1.44) is less than |critical value| (t0.005,45 = 2.690), hence we fail to reject H0 and there is no significant evidence to conclude that there are gender differences in the average number of hours worked per day among employees at a law firm.