A large bank plans an experiment to learnwhether offering cash back on purchases of

Chapter 0, Problem 22.51

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A large bank plans an experiment to learnwhether offering cash back on purchases of gasoline will increase use of its creditcards. The bank wants to be quite certain of detecting a mean increase of = $100 in the amount charged per month, at the = 0.01 significance level. Itmakes the cash back offer to 50 customers and compares their charges for themonths before and after the offer. Find the approximate power of the t test withn = 50 against the alternative = $100 as follows.(a) What is the critical value t for the one-sided test with = 0.01 and n = 50?(b) Write the rule for rejecting H0: = 0 in terms of the t statistic. Then takes = 108 (an estimate based on the banks past experience) and state the rejectionrule in terms of x.(c) Assume that = 100 (the given alternative) and that = 108. Theapproximate power is the probability of the event you found in (b), calculatedunder these conditions. Find the power. Would you recommend that the bank doa test on 50 customers, or should more customers be included?