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.
State $H_0$ and $H_1$ for the test to check
Assuming that annual per employee profit follows a Normal distribution, the resulting P-value for the test is, P= 0.405 (3 d.p.):
Based entirely on this P-value, what would you conclude from the test?
- 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?
- 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 α=0.01 significance level, what would you conclude and why?
- If you chose to reject $H_0$ but $H_0$ was actually true, would you be making a Type I or Type II error?
- What assumptions have you made about the annual per employee profit in this test?