1. The United States Golf Association requires that golf balls have a mean diameter that is 1.68 inches. An engineer for the USGA wishes to discover whether Maxfli XS golf balls have a mean diameter different from 1.68 inches. A random sample of Maxfli XS golf balls was selected; their diameters are shown in the table. Using Minitab, test the claim that the golf balls have a mean diameter that is different from 1.68 inches at the =0.05 level of significance.

1.683	1.677	1.681
1.685	1.678	1.686
1.684	1.684	1.673
1.685	1.682	1.674

2. A dietician claims that the total cholesterol for 40-49 years old males is high. Anyone with a total cholesterol above 200 is considered to have high cholesterol. She conducts a random sample of 40 males between the ages of 40 and 49 years and finds that their mean total cholesterol is 211, with a sample standard deviation (s) of 39.2.

a. Test the dietician's claim that the total cholesterol of males 40-49 years old is more than 200 at a 95% level of confidence (=0.05 level of significance). Show all the steps.

b. Using the p-value, would the answer change if we were testing at 99% Confidence (=.01 level of significance)?

c. Explain what it would mean to make a Type I error.

d. Explain what it would mean to make a Type II error.

3. The EPA publishes data regarding the miles per gallon of all cars. A researcher claims that their company's fuel additive increases the miles per gallon a car will get under highway driving conditions. To perform this experiment, the researcher finds that the mean miles per gallon of all cars manufactured in 1999 without using the fuel additive is 25.1 based on data obtained from the EPA. The researcher then obtains a random sample of 35 different cars manufactured in 1999 and adds the fuel additive. The cars are all driven by the same driver under the same operating conditions. The sample mean is determined to be 26.8 miles per gallon with a sample standard deviation of s=3.9 miles per gallon. At a 95% level of confidence, test the researcher's claim that the fuel additive increases a car's mean gas mileage. Cover all the steps needed for testing.