According to a union agreement, the mean income for all managers in a large manufacturing company equals

$2000 per month. A representative of a graduate group decides to analyze whether the mean income μ for graduate managers matches this norm. For a random sample of 10 graduate employees, ¯y = $1500 and s = 100.

(a) Test whether the mean income of graduate employees differs from $2000 per month. Include assumptions, hypotheses, test statistic, and P-value. Interpret the result.

(b) Report the P-value for Ha:μ < 2000. Interpret.

(c) Report and interpret the P-value for Ha: μ > 2000.

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