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?

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The Answer of 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?

Suppose That the Starting Salaries of Male Workers Are Normally Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​

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