Null Hypothesis and the Alternative Hypothesis

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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.



1. According to the U.S. federal Highway Administration, the mean number of miles driven annually 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 35 drivers is 12,895. Assuming the population standard deviation, σ = 3800 miles, test the agent’s claim at the 1% level of significance.


2. 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 which 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.


3. In 2004, 65% of adult Americans thought that the death penalty was morally acceptable. In a recent 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 2004?

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