# Statistics Test Questions

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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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[25] 2) A list contains 600 names of 300 married couples that donated to a local charity. Names are listed in alphabetic order and assigned numbers 1,2, ... ,600, couple by couple, first husband and then wife. Use the following portion of the table of random numbers 23632 27889 47914 02584 37680 20801 72152 39339 34086 43218 15263 31624 76384 17403 53363 44167 64486 64758 75366 76554 31601 12614 33072 60332 92325 19474 01624 76384 97403 53363 44167 64486 64758 75366 76554 31601 12614 33072 19474 23632 27889 47914 02584 37680 20801 72152 39339 34806 08930 25570 33120 45732 in the following problems: (use some simple procedure and explain it briefly in each of the cases): (a) Select an SRS of 5 couples from the list (give the list numbers of these 10 persons) (b) How would you select an SRS of 5 wives from the list? (c) How would you select an SRS of 5 persons (regardless of the gender) from the list? (d) If you want to estimate the average life of the people in this group, could it be appropriate to use any of the samples from (a), (b), or (c)? Explain. How about estimating the average length of marriage? Solutions: [7] (a) Two numbers from the list are assigned to each couple, i.e. we have 300 pairs. So we need to select 5 pairs out of 300. We may assign random numbers 001, 002 to pair 1, 003, 004 to par 2, …, 599, 600 to pair 300 [3]: Using groups of three digits and, say, the third row, we have from the table digits 016 247 638 497 403 533 couple 015 247 N/A 497 403 533 016 248 N/A 498 404 534 Sample (list numbers): 15, 16, 247, 248, 403, 404, 497, 498, 533, 534. [4] [6] (b) You can select 5 wives in the same way as you have selected 5 couples, and list only wives’ numbers....

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