The annual profit for your organisation last year was £1203, per employee. The average for the sector was £1228 per employee. You need to know if there is evidence that your organisation is not as profitable, on average, as your competitors. The standard deviation for the sector is £104 per employee.
Question 1. State H0 and H1 for the test to check this?
Assuming that annual per employee profit follows a Normal distribution, the resulting P-value for the test is, P= 0.405 (3 d.p.):
Question 2. Based entirely on this P-value, what would you conclude from the test?
Question 3. What is the probability of getting a profit per employee of £1203, or less, when there is no difference between that for your company and the industry average?
Question 4. If your annual per employee profit was such that the test had resulted in a P-value given by P=0.032 and you were testing at the a=0.01 significance level, what would you conclude and why?
Question 5. If you chose to reject H0 but H0 was actually true, would you be making a Type I or Type II error?
Question 6. What assumptions have you made about the annual per employee profit in this test?