Question

1. The federal government is interested in determining whether salary discrimination exists between men and women in the private sector. Suppose a sample of 16 women and 25 men are taken from the population of first-level managers in the private sector. The information is summarized as follows (amounts are in thousands of dollars):

	Women	Men
n	16	25
X¯	$26.4	$33.3
S	$2.6	$3.2

Test H0 : µ1 = µ2  against H1 : µ1 = µ2  where µ1  and µ2  are the mean salary of first level female and

male managers, respectively. Use α = 0.05 and assume equal variances.

	a	Test statistic = −7.22 and fail to reject H0
	b	Test statistic = −2.68 and fail to reject H0
	c	Test statistic = −7.22 and reject H0
	d	Test statistic = −2.68 and reject H0

Answer 1

To test

test statistic is given by

t = -7.22

Decison criteria : Reject Ho if | test statistic | > critical t value

critical t value with n1 + n2 -2 degrees of freedom and level of significance =

since it is a two tailed test we consider

with degrees of freedom 16 + 25 - 2 = 39

critical t = 2.023

therefore | - 7.22 | = 7.22 > 2.023

Reject the null hypothesis

option c is correct

Test statistic = -7.22 , Reject Ho