- It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets.

What is the 90% confidence interval of the

true proportion of teenage boys who have received

speeding tickets?

- Dr. Christina Cuttleman, a nutritionist, claims that the average number of calories in a serving of popcorn is 75. A sample of 50 servings of popcorn yields an average of 78 calories with a standard deviation of 7. Conduct a hypothesis test using the traditional method to determine if evidence exits to reject Dr. Cuttleman’s claim at a = 0.05.

- A recent gasoline survey said the national average price of gasoline was $2.384 a gallon. It was felt that gasoline in Missouri was significantly lower than the national average. A survey of 30 different communities in Missouri found the average price of gasoline to be $2.329 a gallon with a standard

deviation of $0.152. Conduct a hypothesis test using the P-valuemethod with a=.05 to determine if the price of gas in Missouri is less than the national average.

- Melvin says his average golf score is 75. Melvin lies a lot, and you claim his average score is higher than 75. So, you observe his game for a random sample of ten rounds and find that the sample mean is 78 strokes with a sample standard deviation of 4 strokes. At the .05 level should you believe Melvin or have him barred from the country club?

- U.C.L.A. states that at least 40% of the students live on campus. From a sample of 250 students, 90 live on campus. Does this sample provide evidence that fewer than 40% live on campus? Conduct the test with a=0.01.

- John Davis, a manager of a supermarket, wants to

estimate the proportion of customers that will be using food stamps at his store. How large a sample is required to estimate the true proportion to within 5% with 90% confidence?

## This question was asked on May 13, 2010.

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