Important Question. Need help in checking if I got it right.

A study was conducted to determine if the salaries of the professors from two neighbouring universities were equal. A sample of 20 professors from each university was randomly selected. The mean from the first university was $109,100 with a population standard deviation of $2300. The mean from the second university was $110,500 with a population standard deviation of $2100. Assume that the distribution of professor salaries, at both universities, are approximately normally distributed. Level of significance = 0.05.

a. Using the critical value approach test the claim that the salaries from both universities are equal. Include all key steps of the test.

b. Use the four-step P-value approach and test the claim that the salaries from both universities are equal.

c. Are the conditions met for using this test?