Question

The table below lists the earnings (in thousands of dollars) of a random sample of 12 male and 12 female salespersons. At alpha = 0.10 can you conclude that there is a difference between males’ and females’ earnings?

Male	28	43	64	51	48	44	36	45	67	49	40	65
Female	36	27	51	43	35	48	41	37	34	47	50	43

The claim is “there is a difference between males’ and females’ earnings”

Answer 1

1) null and alternate hypothesis

H0:

H1:

2) level of significance = 0.10

3) test statistics

For malw

  N1: 5

df1 = N - 1 = 6 - 1 = 5
M1: 46.33
SS1: 689.33
s21 = SS1/(N - 1) = 689.33/(6-1) = 137.87


For female

N2: 6
df2 = N - 1 = 6 - 1 = 5
M2: 40
SS2: 404
s22 = SS2/(N - 1) = 404/(6-1) = 80.8


T-value Calculation

s2p = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((5/10) * 137.87) + ((5/10) * 80.8) = 109.33

s2M1 = s2p/N1 = 109.33/6 = 18.22
s2M2 = s2p/N2 = 109.33/6 = 18.22

t = (M1 - M2)/√(s2M1 + s2M2) = 6.33/√36.44 = 1.05

4) p value = 0.3188

5) since p value is greater than level of significance so we fail to reject H0

6) so there insufficient evidence to conclude that there is a difference between males and females earning.