A company that produces and markets video game systems wishes to assess its cust

Question

A company that produces and markets video game systems wishes to assess its customers' level of satisfaction with a relatively new model, the XYZ-Box. In the six months since the introduction of the model, the company has received 73,219 warranty registrations from purchasers. The company will select a random sample of 65 of these registrations and will conduct telephone interviews with the purchasers. Specifically, each purchaser will be asked to state his or her level of agreement with each of the seven statements listed on the survey instrument given in the following table. Here, the level of agreement for each statement is measured on a 7-point Likert scale. Purchaser satisfaction will be measured by adding the purchaser's responses to the seven statements. It follows that for each consumer the minimum composite score possible is 7 and the maximum is 49. Furthermore, experience has shown that a purchaser of a video game system is "very satisfied" if his or her composite score is at least 42. Suppose that when the 65 customers are interviewed, their composite scores are as given in the following table. Using the data, estimate limits between which most of the 73.219 composite scores would fall. Also, estimate the proportion of the 73.219 composite scores that would be at least 42. (Round your proportion of scores answer to 3 decimal places.)

Explanation / Answer

For the given data:

Sample mean = 41.46

SD = 3.4

Thus, most of the scores should fall between +/- 3 S.D of the mean.

i.e scores would lie between

lower limit = 41.46 - 3(3.4) =31.26

upper limit = 41.46 + 3(3.4) = 51.66

However, the upper limit can't be beyond 49 which is the maximum possible score.

Hence. the limits would be between 31 and 49.

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