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?

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Definitions:

Materials Price Standard

The predetermined cost of materials that should be incurred under efficient operating conditions.

Predetermined Overhead Rate

A rate calculated before a period begins, used to allocate estimated overhead costs to products or services based on a chosen activity base.

Standard Activity Index

A benchmark used to measure the amount of activity, productivity, or performance in a given scenario, often compared to an industry standard.

Budgeted Overhead Costs

The estimated costs related to the indirect aspects of manufacturing or service delivery that are planned for a specific period.