Refer to given Exercise. Suppose that allegations were made that the (unknown) population mean salary of women who work in that job is lower than the known population mean salary of $80,000 for men.
a. Does the sample information for the 100 women in given Exercise support that allegation? Explain.
b. The question in part (a) is an example of hypothesis testing, the goal of which was described in Section 9.1 as "to reject the notion that chance alone can explain the sample results." Explain how the question in part (a) fits that description of hypothesis testing.
Exercise
The mean salary for a population of women who work in a traditional male job is $80,000. A random sample of 100 women is taken from this population and the sample mean and standard deviation are found to be = $78,000 and s = $4000.
a. Compute the standardized statistic for the sample mean in this situation.
b. Draw a picture of the appropriate distribution for the standardized statistic, and find the area below the value of the standardized statistic computed in part (a).
(Note: The use of either statistical software or Excel is necessary.)