According to union agreement, the mean income for all senior-level assembly-line workers in a large company equals 500 dollars per week. A representative of a woman'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.) We can be 95% confident that x bar is between 371 and 509