Question

I have completed a. of this problem, but do not know how to proceed with b. If someone could explain how to do part b in some detail?

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.

1. Using the critical value approach test the claim that the salaries from both universities are equal. Include all key steps of the test. [10 marks]
2. Use the four-step P-value approach and test the claim that the salaries from both universities are equal. [10 marks]
3. Are the conditions met for using this test? [3 marks]

Answer 1

b)The sample means are . The population standard deviations are

and sample sizes are .

Since, the population standard deviations are are known, we use z-distribution.

The test statistics is

The P-value of the test is

Since  , we reject the null hypothesis that the mean are equal.

We conclude with 95% confidence that the two salaries are different.