A certain manufacturing firm produces a product that is packaged under two brand names, for

marketing purposes. These two brands serve as strata for estimating potential sales volume

for the next quarter. A SRS of customers for each brand is contacted and asked to provide

a potential sale figure y (in number of units) for the coming quarter. Last year's true sales

figure, for the same quarter, is available for each of the sampled customers and is denoted by x.

The data are given in the accompanying table. The sample for brand I was taken from a list of

120 customers for whom the total sales in the same quater of last year was 24,500 units. The

brand II sample come from 180 customers with a total quarterly sales last year of 21 200 units.

Brand I

xi yi

204 210

143 160

82 75

256 280

275 300

198 190

Brand II

xi yi

137 150

189 200

119 125

63 60

103 110

107 100

159 180

63 75

87 90

Use R to do the following questions.

For each question, report the R code, the R output, and your answer.

(2 marks) Find a basic estimate (without auxiliary information) of the total potential

sales. Estimate the variance of your estimator.

(Part 2) (6 marks) In this part, use the Separate Ratio Method (SR) to answer

(a) (2 marks) Find a ratio estimate of the total potential sales. Estimate the variance

of your estimator.

(b) (2 marks) Find a regression estimate of the total potential sales. Estimate the

variance of your estimator.

(c) (2 mark) Which of the methods in (Part 1), (Part 2, (a) and (b)) do you recommend?

(Part 3) (5 marks) In this part, use the Combined Ratio Estimator Method (CR) to answer the

following questions:

(a) (2 marks) Find a ratio estimate of the total potential sales. Estimate the variance

of your estimator.

(b) (2 marks) Find a regression estimate of the total potential sales. Estimate the

variance of your estimator.

(c) (1 mark) Which of the methods in (a) and (b) of (Part 3) would you suggest?

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