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# Hypothesis testing

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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 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.

##### 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 ...

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• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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