8.38 Wage discrimination? According to a union agreement, the mean income for all senior-level assembly-line workers in a large company equals $500 per week. A representative of a women’s group decides to analyze whether the mean income for female employees matches this norm.

For a random sample of nine female employees, using software, she obtains a 95% confidence interval of (371, 509). Explain what is wrong with each of the following interpretations of this interval.

a. We infer that 95% of the women in the population have income between $371 and $509 per week.

b. If random samples of nine women were repeatedly selected, then 95% of the time the sample mean income would be between $371 and $509.

c. We can be 95% confident that x is between $371 and $509.

d. If we repeatedly sampled the entire population, then 95% of the time the population mean would be between $371 and $509.