# Question: A variety of stores offer loyalty programs Participating shoppers swipe

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 s = +40. (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 p-value of the test. Do the data supply enough evidence to reject the null hypothesis if α = 0.05?

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