Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, μ, spent by customers at the supermarkets has been reported to be 38
Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses as indicated.
(a) What are the null hypothesis, H0, and the alternative hypothesis, H1, that the consultant should use for the test?
(b) Assuming that the actual value of μ is 43 minutes, what is the probability that the consultant accepts the null hypothesis? Round your response to two or more decimal places.
(c) What is the probability that the consultant commits a Type Ⅰ error? Round your response to two or more decimal places.
(d) Suppose that the consultant decides to perform another statistical test using the same population, the same null and alternative hypotheses, and the same sample size, but for this second test the consultant uses a significance level of 0.1 instead of a significance level of 0.05. Assuming that the actual value of μ is 43 minutes,how does the power of this second test compare to the power of the original test?
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