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Hypothesis Testing Worksheet 1. Suppose an experiment is run to determine if a father’s weight is different from their college age son’s weight. 68 males had their weights recorded along with their father’s. The sample mean of the differences was -17 pounds with a standard deviation of 33 pounds. a. Do a hypothesis test at the alpha = 0.05 level to see if the difference is truly significant. (Use the 7-steps and show your work for all steps.) Ho: Mdiff=0 vs Ha: Mdiff (not=) 0 Assumptions assumed met, t=-17/(33/sqrt(68)) = -4.248048 p-value < 0.001 Reject Ho in favor of Ha At the 5% significance level, there is enough evidence to reject the null that the weights are the same for father and college age son in favor of the alternative that the weights are different. b. Calculate a 95% confidence interval for the true mean difference. How is the interpretation of your C.I. related to your conclusion from (d)? -17 +/- 2*33/sqrt(68) = (-25, -9) The interpretation is: we are 95% confident the true value lies between -25 and 9 lbs. Since 0 is not in this interval it is not a value we believe to be a possibility for Mdiff. We also used the same significance value (alpha) and rejected 0 as a legitimate value in our hypothesis test.

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2. Suppose the Michelin tire company interested in showing that a certain type of their tires last longer than 30,000 miles. They take a random sample of size n=25.
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