Question: Suppose a candidate running for sheriff claims that she will reduce the average speed of emergency response to less than 30 minutes. (30 minutes is thought to be the average response time with the current sheriff.) There are no past records, so the actual standard 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 for the 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 five steps of hypothesis testing.
(b) Illustrate your answer with a histogram of the sample's scores and sketches of the population distribution and the distribution of means, showing the t score and cutoff points for significance.
(c) Explain your answer to someone who has never taken a course in statistics.