Statistics

A customer is considered to be very satisfied with his or her XYZ Box video

game system if the customer’s composite score on the survey instrument is at

least 42. One way to show that customers are typically very satisfied is to show

that the mean of the population of all satisfaction ratings is at least 42. Letting

this mean be µ, in this exercise we wish to investigate whether the sample of 65

satisfaction ratings provides evidence to support the claim that µ exceeds 42

(and, therefore, is at least 42).

Assume that µ equals 42. It is attempted to use the sample to contradict this

assumption in favour of the conclusion that µ exceeds 42. Recall that the mean

of the sample of 65 satisfaction ratings is �̅ = 42.95 , and assume that σ, the

standard deviation of the population of all satisfaction ratings, is known to be

2.64.

a) Consider the sampling distribution of �̅ for random samples of 65

customer satisfaction ratings. Determine the probability of observing a

sample mean greater than or equal to 42.95 when we assume that µ

equals 42.

b) If µ equals 42, what percentage of all possible sample means is greater

than or equal to 42.95?