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.

The Video Game Satisfaction Survey Instrument
	Strongly						Strongly
Statement	Disagree						Agree
The game console of the XYZ-Box is well designed.	1	2	3	4	5	6	7
The game controller of the XYZ-Box is easy to handle.	1	2	3	4	5	6	7
The XYZ-Box has high-quality graphics capabilities.	1	2	3	4	5	6	7
The XYZ-Box has high-quality audio capabilities.	1	2	3	4	5	6	7
The XYZ-Box serves as a complete entertainment center.	1	2	3	4	5	6	7
There is a large selection of XYZ-Box games to choose from.	1	2	3	4	5	6	7
I am totally satisfied with my XYZ-Box game system.	1	2	3	4	5	6	7

Suppose that when the 65 customers are interviewed, their composite scores are as given in the following table.

Composite Scores for the Video Game Satisfaction Rating Case
39	44	46	44	44
45	42	45	44	42
38	46	45	45	47
42	40	46	44	43
42	47	43	46	45
41	44	47	48
38	43	43	44
42	45	41	41
46	45	40	45
44	40	43	44
40	46	44	44
39	41	41	44
40	43	38	46
42	39	43	39
45	43	36	41

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 2 decimal places.)

Most of the scores would fall between....and....

An estimate of the proportion of scores that would be at least 42 =.....%.

Answer 1

Dear your satisfaction is more important,I provided answers with detailed explanation. If you are satisfied with my explanations please THUMBS UP.. Thanks inadvance for your support dear....

We can use. Confidence Interval technique to find out limit. Since we are unaware about population variance , I used t distribution to find 95% confidence interval.