Refer to the analysis of shoppers in Exercise 45.

(a)  If several of those participating in the loyalty program are members of the same family, would  this cause you to question the assumptions that  underlie the test in this question?

(b)  Several outliers were observed in the data for the loyalty program. Should these high-volume  purchases be excluded?

Exercise 45

A variety of stores offer loyalty programs. Participating shoppers swipe a bar-coded tag at the register  when checking out and receive discounts on certain purchases. Stores benefit by gleaning information  about shopping habits and hope to encourage shoppers to spend more. A typical Saturday morning  shopper who does not participate in this program spends $120 on her or his order. In a sample of 80  shoppers participating in the loyalty program, each shopper spent $130 on average during a recent  Saturday, with standard deviation . (See the histogram on the next page.) Is this statistical proof  that the shoppers participating in the loyalty program  spend more on average than typical shoppers?   (Assume that the data meet the sample size condition.)

(a)  State the null and alternative hypotheses.   Describe the parameters.

(b)  Describe the Type I and Type II errors.

(c)  How large could the kurtosis be without violating the CLT condition?

(d)  Find the -value of the test. Do the data supply enough evidence to reject the null hypothesis if  ?