SmallBatchCheese Co. want to test if their new advertising campaign has improved sales at the 10 local stockists they use.

a) [1 mark] What null hypothesis should they use?

b) [2 mark] What alternative hypothesis should they use? Explain why you think a one or two-sided test is most appropriate in this case.

They sample their 10 stockists and find mean sales x = 83.1 cheeses/quarter compared a previous long-run average of 64.4 cheeses/quarter. The sample standard deviation was found to be s = 29.5.

c) [3 marks] How many standard deviations away from the value predicted by the null hypothesis is the sample mean? Show your working.

d) [2 marks] Does the test statistic you calculated in part (c) follow a t or a z distribution. Explain your choice.

e) [2 marks] The p-value is calculated to be 0.038. Interpret what this means in the context of this scenario.