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, \mu , spent by customers at the supermarkets has been reported to be 36 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that \mu is less than 36 minutes. the consultant plans to do a statistical test and collects a random sample of 50 shopping times at the supermarkets.
suppose that the population of shopping times at the supermarkets has a standard deviation of 10 minutes and that the consultant performs her hypothesis test using the 0.05 level of significance.
based on this information, answer the questions below. carry your intermediate computations to at least four decimal places, and round your responses as indicated.
what are the null and alternative hypotheses that the consultant should use for the test?
h0: \mu is: less less than or equal greater greater than or equal not equal equal to
50,10, 36, or 32
h1: \mu is: less than or equal greater greater than or equal not equal equal to
50,10, 36, or 32
assuming that the actual value of u is 32 minutes, what is the power of the test?
(round your response to at least two decimal places.)
?
what is the probability that the consultant rejects the null hypothesis when, in fact, it is true?
(round your response to at least two decimal places.
?
suppose that the consultant decides to perform another statistical test using the same population, the same null and alternative hypothesis, and the same level of significance, but for this second test the consultant chooses a random sample of size 100 instead of a random sample size of 50. assuming that the actual value of u is 32 minutes, how does the probability that the consultant commits a type ii error in this second test compare to the probability that the consultant commits a type ii error in the original test? choose one
a. the probability of committing a type ii error in the second test is greater
b. the probability of committing a type ii error in the second test is less.
c. the probabilities of committing a type ii error are equal