Problem 1. Salaries (23 marks) A study was conducted to determine if the salarie

Question

Problem 1. Salaries (23 marks) 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. [10 marks]

b) Use the four-step P-value approach and test the claim that the salaries from both universities are equal. [10 marks]

c) Are the conditions met for using this test? [3 marks]

Explanation / Answer

(a)

Critical value = 2.33

Test statistic =1.71

(b) p value = 0.5365

(c)

Do not reject the null hypothesis ..

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