Question

You may need to use the appropriate appendix table or technology to answer this question.

The gap between the earnings of men and women with equal education is narrowing but has not closed. Sample data for seven men and seven women with bachelor's degrees are as follows. Data are shown in thousands of dollars.

Men	Women
39.6	46.5
82.5	42.4
52.2	38.9
60.2	49.5
47.2	32.8
53.9	58.5
62.3	26.8

(a)

What is the median salary (in $) for men? For women?

men$ women$

(b)

Use α = 0.05 and conduct the hypothesis test for identical population distributions.

State the null and alternative hypotheses.

H₀: The two populations of salaries are identical.
H_a: The two populations of salaries are not identical.H₀: Median salary for men − Median salary for women > 0
H_a: Median salary for men − Median salary for women = 0    H₀: Median salary for men − Median salary for women ≤ 0
H_a: Median salary for men − Median salary for women > 0H₀: The two populations of salaries are not identical.
H_a: The two populations of salaries are identical.H₀: Median salary for men − Median salary for women ≥ 0
H_a: Median salary for men − Median salary for women < 0

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the annual salaries of men and women.Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the annual salaries of men and women.    Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the annual salaries of men and women.Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the annual salaries of men and women.

Answer 1

We will use MINITAB software to get the answer

there we will use Mann Whiteney Test for two sample median

the MINITAB output is

a)

From the above output we get

median : Men=59.9 ; Women=42.4

b)

H0: Median salary for men − Median salary for women ≤ 0
Ha: Median salary for men − Median salary for women > 0

W=69

p-value=0.0409

What is your conclusion?

Reject H0. There is sufficient evidence to conclude that there is a significant difference between the annual salaries of men and women

since p-value = 0.0409<0.05

conclusion :