(a) What is the median salary (in $) for men? For women? (b) Use ? = 0.05 and conduct the hypothesis test for identical population distributions. State the null and alternative hypotheses. - H0: The two populations of salaries are not identical. Ha: The two populations of salaries are identical - H0: Median salary for men − Median salary for women > 0 Ha: Median salary for men − Median salary for women = 0 - H0: Median salary for men − Median salary for women ≥ 0 Ha: Median salary for men − Median salary for women < 0 - H0: The two populations of salaries are identical. Ha: The two populations of salaries are not identical. - H0: Median salary for men − Median salary for women ≤ 0 Ha: Median salary for men − Median salary for women > 0 * Find the value of the test statistic W and the p-value. (Round your answer to four decimal places.) c, What is your conclusion? - Do not 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 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. - Reject H0. There is not sufficient evidence to conclude that there is a significant difference between the annual salaries of men and women.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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7. 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
31.6	44.5
86.5	46.4
56.2	30.9
68.2	41.5
47.2	36.8
59.9	50.5
66.3	24.8

(a)

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

(b)

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

State the null and alternative hypotheses.

- H₀: 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

- H₀: Median salary for men − Median salary for women ≥ 0

H_a: Median salary for men − Median salary for women < 0

- 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

* Find the value of the test statistic W and the p-value. (Round your answer to four decimal places.)

c, What is your conclusion?

- Do not 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 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.

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

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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