A company that produces and markets video game systems wishes to assess its customers level of satisfaction

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 randomly select 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 Figure 1.7. 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 €œvery satisfied€ if his or her composite score is at least 42.

Figure 1.7

The Video Game Satisfaction Survey Instrument FIGURE 1.7 Strongly Strongly Disagree Statement The game console of the XY

a. Assume that the warranty registrations are numbered from 1 to 73,219 in a computer. Starting in the upper left corner of Table 1.4(a) and moving down the five leftmost columns, we see that the first three five-digit numbers obtained are 33276, 03427, and 92737. Starting with these three random numbers and moving down the five leftmost columns of Table 1.4(a) to find more five-digit random numbers, use Table 1.4(a) to randomly select the numbers of the first 10 warranty registrations to be included in the sample of 65 registrations.

TABLE 1.4 Random Numbers (a) A portion of a random number table 33276 85590 79936 56865 05859 90106 78188 90511 27156 03

b. Suppose that when the 65 customers are interviewed, their composite scores are as given in Table 1.8. Using the largest and smallest observations in 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.