9.19 A college canteen has a selection of pre-packed sandwiches on sale. The prices of each of the 10 types of sandwich on sale and the number sold on a single day selected at random were:

Price (£) 1.20 1.30 1.35 1.40 1.55 1.60 1.75 1.90 2.05 2.10 Sales 27 23 20 24 17 14 7 12 3 6

(a) Find the best-fit regression model and test the null hypothesis that the slope of the population line of best fit is zero using a 1 per cent level of significance.

(b) Obtain 99 per cent confidence intervals for the mean sales of sandwiches that cost (i) £1.80, and (ii) £2.75.
Which of these estimates is likely to be the more reliable, and why?