Sheriff candidate claims reduction emergency response time
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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. (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.
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Solution Summary
Five-step hypotesis tests illustrates answer with a histogram of sample scores and sketches the population distribution and the distribution of means, showing the t score and cutoff points for significance.
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Hypothesis about the Population:
Population 1: The new sheriff will reduce the average speed of emergency response to less than 30 minutes.
Population 2: The old sheriff time of an average speed of emergency response of 30 minutes.
Research hypothesis: The new sheriff will reduce the emergency response to less than 30 minutes.
Null hypothesis: The new sheriff's response time will not significantly change from the old sheriff's response time ...
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