Question 3 (4 + 6 = 10 marks)

a)A certain pay television company wishes to estimate the proportion of its customers who would purchase a pay television program guide. To , the company manager decides to select a random sample of customers and note the number who would purchase a program guide.

b)The research director of a large supermarket chain wished to measure the effect of a storewide sales campaign on sales of non-sale items and believes that sales of non-sale items may also be affected by the overall average weekly sales volume of the store.

He randomly selected 10 stores and then, another 10 stores that matches the first 10 according to average weekly sales volume. The results, after pairing, are shown in the following table

Assuming that all sales of non-sale items are normally distributed regardless of the campaign, use the above information to test whether sales of non-sale items are significantly higher with the sales campaign than without. Take a = 0.05.

Note: You may use the following summary values when answering this question - The sample of differences in the above table has a mean of 3.65 and a standard deviation of 3.428.

Matched Sales of non-sale items with Sales of non-sale items Differences pair sales campaign, (x) without sales campaign, (y) d = (x y) 1.9 1 2 3 4 5 6 7 8 9 _x O