Suppose a candidate running for sheriff in a rural community claims that she will reduce the average speed of emergency response to less than 30 minutes, which 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 minutes. Using the .05 level of significance, did she keep her promise?
(a) Use the steps of hypothesis testing.
b) Sketch the distributions involved.
(c) Explain your answer to someone who has never taken a course in statistics.