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Hypothesis Testing: Average Speed

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.

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Solution Preview

(a) Go through the five steps of hypothesis testing.

This is a simple one-sided t-test.
Step 1: State the null and alternative hypotheses
The null hypothesis, Ho: The average speed of emergency response is not less than 30 minutes.
Alternative Hypothesis, Ha: The average speed of emergency response is less than 30 minutes.

- Refer to the attached document ...

Solution Summary

This solution provides a step by step response which clearly indicates how to complete this hypothesis test and solve for the test statistic. A Word document also accompanies this solution and presents the full solution, including all calculations and equations.