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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 statistically significant 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 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?