QUESTION FIVE (20 Marks)

a) A shopkeeper wanted to investigate whether or not there was a correlation

between the prices of food 10 years ago in 1992, with their prices today. He chose 8

everyday items and the prices are given in the table below.

sugar milk eggs rolls tea bags coffee potatoes flour

1992 price $1.44 $0.80 $2.16 $1.80 $0.92 $3.16 $1.32 $ 1.12

2002 price $2.20 $1.04 $2.64 $3.00 $1.32 $2.28 $1.92 $1.44

(a) Calculate the mean and the standard deviation of the prices

(i) in 1992;

(ii) in 2002.

(b)

(i) Given that sxy = 0.3104, calculate the correlation coefficient.

(ii) Comment on the relationship between the prices.

(c) Find the equation of the line of the best fit in the form y = mx + c.

(d) What would you expect to pay now for an item costing $2.60 in 1992?

(e) Which item would you omit to increase the correlation coefficient?