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# Hypothesis testing

5. In the past it took Kim 148.4 seconds to swim 200 meters. Kim wants to know if her average has changed. She records her time on 50 randomly selected occasions and computes the mean to be 147.8 seconds with a standard deviation of 2.3 seconds.
a. Perform the appropriate test of hypothesis to determine whether Kim's average time has changed. Use alpha=.01.
b. Compute the power of the test if Kim's actual mean swimming time is 147.3 seconds. Interpret the results.

#### Solution Preview

Solution. Let us define two hypothesis. Ho: u=u0=148.4, H1: u is not equal to 148.4. We have the mean of sample x^=147.8, and the standard deviation s=2.3, n=50, alpha=0.01, t_0.005(50)=2.66. We can get the ...

#### Solution Summary

5. In the past it took Kim 148.4 seconds to swim 200 meters. Kim wants to know if her average has changed. She records her time on 50 randomly selected occasions and computes the mean to be 147.8 seconds with a standard deviation of 2.3 seconds.
a. Perform the appropriate test of hypothesis to determine whether Kim's average time has changed. Use alpha=.01.
b. Compute the power of the test if Kim's actual mean swimming time is 147.3 seconds. Interpret the results.

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