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STA 304H1F-1003H Winter 2020
Assignment 2-Question 3
Question 3. ( 13 marks)
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.
Use R to do the following questions.
For each question, report the R code, the R output, and your answer.
(Part 1) (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 mean 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 (Part 1), (Part 3, (a) and (b)) would you suggest?

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