Question: (22 points) After training intensively for six months, John hopes that his mean time to run 100m has decreased from last year’s mean time of 12.2 seconds. He performs a hypothesis test to determine whether his mean time has decreased. Preliminary data indicate that it is reasonable to apply a z-test with s = 0.35 seconds.

1. What is the power of the hypothesis test to detect a decrease in mean time of 0.1 seconds if n=30 and a = 0.10?
2. Which of the following would cause the power of the test to increase, compared to part (a)? (Circle/underline all that apply.)

1. increasing the sample size
2. increasing the significance level
3. increasing the standard deviation
4. increasing the time between samples

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