30409S_T1sol.pdf

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6 Feb 2013
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STA 304H1 F/1003H F SUMMER 2009, First Test, May 28 (20%)
Duration: 50min. Allowed: hand-calculator, aid-sheet, one side, with theoretical
formulas and definitions only.
[25] 1) A marketing analyst is asked to study the buying habits of shoppers at a national
chain store (e.g. Sears). Suppose there are 150 stores around the country.
(a) Describe the population of interest.
(b) Describe in short a realistic sampling procedure for obtaining a representative sample
in this problem, and give a name of the procedure.
(c) Are the target population and sampled population the same? Explain some related
problems.
(d) Give two variable of interest related to element of the population (one quantitative,
the other qualitative).
(e) Describe an appropriate method of data collection in this study.
Solutions:
[5](a) All shoppers at the chain store. More accurate definition would be: All shoppers
that regularly shop at the chain store, but then it should require to defining who is a
“regular shopper”. The definition may also include a time period of shopping. [5]
[7](b) Two stage cluster sampling: First select an SRS of stores, and then a sample of
customers, e.g. when entering the store, or at exit, using systematic sampling, because a
list of shoppers does not exist. [7] Selecting customers from each store is possible but
would be inconvenient and much more costly. Also, the sampling design may include a
rule of selecting a sampling day at the store. Sampling at the same day at every store may
produce a bias result. It is also possible to send a questionnaire to the registered
customers (most of them may have the chain’s membership card), but this would also be
very costly and with a large nonresponse rate.
[6](c) They are not the same. If the sample is taken from the shoppers present at stores,
that the sampling population is much smaller that the target population. If the sample is
taken from registered shoppers, many shoppers may not be registered. [6]
[4](d) Quantitative: amount of money spent in one visit/a year, number of items
purchased, … Qualitative: item of primary interest, items of interest found, satisfaction,
[4]
[3] (e) A short personal interview, or short questionnaire filled in at the spot. [3]
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