Suppose small business profit per week in Tasmania has been, on average, $6000 per week in the past. A business consultant would like to know if profit has decreased. She collects a random sample of 36 business and find the average weekly profit is $5760 with a standard question deviation $935. Assume the conditions are satisfied, and do NOT need to be checked.

a) Write the hypotheses to test the consultant's claim.

b) Give the calculated test statistic value for this test.

c) Give the critical value for this test, at a level of = 0.10,

d) Give your decision.

e) Give your conclusion, in the context of this question.

f) Briefly explain if your decision changes if you were now told to use = 0.05.