According to a union agreement, the mean income for all senior-level workers in a large service company equals $500 per week. A representative of a women’s group decides to analyze whether the mean income μ for female employees matches this norm. For a random sample of nine female employees, ¯y = $410 and s = 90.

(a) Test whether the mean income of female employees differs from $500 per week. Include assumptions, hypotheses, test statistic, and P-value. Interpret the result.

(b) Report the P-value for Ha:μ < 500. Interpret.

(c) Report and interpret the P-value for Ha: μ > 500.

(Hint: The P-values for the two possible one-sided tests must sum to 1.)