6. For 30 female assistant professors selected at random from arts and science departments in a large state university system, the mean academic year salary is $41,000 The mean salary for a random sample of 50 male assistant professors is $41.800. The sample stand- ard deviations are $3000 for females and $3400 for males.

a) Construct a 95% confidence interval for the difference in mean salary between male and feinale assistant professors in this system. Interpret.

b) Perfonn a significance test of whether the true means are identical. Interpret the P- value

c) What decision would you make in the test, using a 05? Explain how this decision relates to information displayed by the confidence interval.