Question

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 $140 on her or his order. In a sample of 70 shoppers participating in the loyalty program, each shopper spent $150 on average during a recent Saturday, with standard deviation s = $40. 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.) Complete parts a-d. (a) State the null and alternative hypotheses. Describe the parameters. Choose the correct answer below. A. Hoiu s $140 vs Hau >$140; u is the average spent by a shopper in the loyalty program. O B. Ho: u 2 $140 vs Ha: u<$140; u is the average spent by a shopper not in the program. C. Hoius $140 vs Ha: u > $140; u is the average spent by a shopper not in the program. O D. Ho: u 2 $140 vs Ha: u < $140; u is the average spent by a shopper in the loyalty program. (b) Describe the Type I and Type II errors. Choose the correct answer below. A. Concluding that loyal shoppers spend more when in fact they do not is a Type I error. Concluding that loyal shoppers do not spend more when in fact they do is a Type II error. O B. Concluding that loyal shoppers spend more when in fact they do not is a Type I error. Concluding that loyal shoppers do not spend more and they do not is a Type II error. O C. Concluding that loyal shoppers do not spend more when in fact they do is a Type I error. Concluding that loyal shoppers spend more when in fact they do not is a Type II error. O D. Concluding that loyal shoppers spend more and they do is a Type I error. Concluding that loyal shoppers do not spend more when in fact they do is a Type II error. (c) How large could the kurtosis be without violating the CLT condition? KA must be less than

Answer 1

n = 70

c) Number of kurtosis without violation the CLT condition is :

n > 10 * |K₄|

70 > 10 * |K₄|

K₄ < 7

K₄ must be less than 7