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# Suppose a candidate running for sheriff claims that she will reduce the average speed of emergency response to less than 30 minutes.

Suppose a candidate running for sheriff claims that she will reduce the average speedof emergency response to less than 30 minutes. (30 minutes is thought to be the averageresponse time with the current sheriff.) There are no past records, so the actualstandard deviation of such response times cannot be determined. Thanks to this campaign,she is elected sheriff, and careful records are now kept. The response times forthe first month are 26, 30, 28, 29, 25, 28, 32, 35, 24, and 23 min.Using the .05 significance level, did she keep her promise? (a) Go through the fivesteps of hypothesis testing. (b) Illustrate your answer with a histogram of the sample’sscores and sketches of the population distribution and the distribution of means, showingthe t score and cutoff points for significance. (c) Explain your answer to someonewho has never taken a course in statistics.