Solve the below problem:
Q: A population of women who work in a traditional male job have a mean salary of $80,000 with a standard deviation of $4,000. Suppose the mean salary for the population of men who work the same traditional male job is $81,000 with a standard deviation of $5,000. Allegations are made that the mean salary for women is lower than that for men. To investigate these allegations, researchers plan to take a random sample of 25 women and 25 men from these populations and calculate the difference in sample means (men - women).
a. What is the mean of the difference in sample means?
b. What is the standard deviation of the difference in sample means?
c. Draw a picture of the sampling distribution of the difference in sample means. (Be sure to label thex-axis and indicate its scale.)
d. What is the probability that the sample mean salary for women will begreater than or equal tothe sample mean salary for men?