Statistics Questions

Question One
A Gallup poll conducted during May 20 – 22, 2005, asked 1006 Americans, “During the past year, about how many books, either hardcover or paperback, did you read either all or part of the way through?” Results of the survey indicated that the mean of the sample was 13.4 books with a standard deviation of 16.6 books. Construct a 99% confidence interval for the mean number of books Americans read either all or part of during the past year.

Question Two
For a random sample of 10 fifth generation iPod music players, the mean battery life was 9.47 hours with a standard deviation of 2.14 hours.

a. Construct a 95% confidence interval for the mean number of hours the batteries will last on these players.

b. Suppose you wanted more accuracy, what could you do to increase the accuracy of the interval without changing the level of confidence?

For the following problems:
1. State the Null Hypothesis and the Alternative Hypothesis
2. Determine the test statistic.
3. Determine the P-value
4. Make a decision regarding the hypotheses based on the P-value and the Level of Significance.

Question Three
According to the U.S. federal Highway Administration, the mean number of miles driven annually by Americans is µ=12,200. An insurance agent in Montana believes that the mean number of miles driven by the residents of his state is higher than the national average. A random sample of 35 drivers is taken from the list of registered drivers in the state of Montana. The mean number of miles driven by the 70 drivers is 12,895. Assuming the population standard deviation, σ = 3800 miles, test the agent’s claim at the 1% level of significance.

Question Four
The United States Golf Association requires that golf balls have a diameter that is 1.68 inches. An engineer for the USGA wishes to determine whether Maxfli XS golf balls have a mean diameter that is different from the 1.68. A random sample of 12 Maxfli XS golf balls was chosen. The mean diameter of the sample was 1.6809 with a standard deviation of 0.0044. Test the engineer’s claim at the 5% level of significance.

Question Five
In 2010, 65% of adult Americans thought that the death penalty was morally acceptable. In a poll conducted by the Gallup Organization, a simple random sample of 1005 adult Americans resulted in 704 respondents stating that they believe the death penalty was morally acceptable when asked, “Do you believe the death penalty is morally acceptable or morally wrong?” (The choices, “morally acceptable” and “morally wrong” were randomly interchanged in the question for each interview.) Is there significant evidence at the 5% level of significance to indicate that the proportion of adult Americans who believe the death penalty is morally acceptable, has increased from the level reported in 2010?

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