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

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 $52,000. The mean salary for a random sample of 50 male assistant professors is $52,800. The same standard deviation are $3000 for females and $3400 for males. a. Construct a 95% confidence interval for the difference in mean salary between male and female assistant professors in this system. Interpret. b. Use the CI in part a to determine what decision you would make in a 2- sided test, using α= 0.05 solution