Suppose That the Starting Salaries of Male Workers Are Normally $\bar { X } _ { 1 } - \bar { X } _ { 2 }$

question 31

Essay

Suppose that the starting salaries of male workers are normally distributed with a mean of $56 000 and a standard deviation of $12 000. The starting salaries of female workers are normally distributed with a mean of $50 000 and a standard deviation of $10 000. A random sample of 50 male workers and a random sample of 40 female workers are selected.
a. What is the sampling distribution of the sample mean difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ ? Explain.
b. Find the expected value and the standard error of the sample mean difference.
c. What is the probability that the sample mean salary of female workers will not exceed that of the male workers?

---

Definitions:

Open Shop Movement

A movement aimed at ensuring that employment is not conditional upon union membership, allowing workers the choice to join a union or not.

Well-Meaning Workers

Refers to employees who have good intentions and aim to perform their duties ethically and proficiently, contributing positively to their work environment.

IWW

The Industrial Workers of the World, an international labor union founded in 1905, advocating for worker solidarity and the abolition of the wage system.

AFL

The American Federation of Labor, a historic national federation of labor unions in the United States, part of the later merger that formed the AFL-CIO.