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Stats Professor Exam 3
2. Allstate Insurance claims that the average commute distance is less than 15 miles. Twenty-six randomly selected commuters are surveyed, and it is found that they drove an average of 14.4 miles during their commute. Their standard deviation was 7.2 miles. Test All State’s claim at the 5% significance level.
3. To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of tar found in all brands of cigarettes. For a particular brand of cigarette, FDA tests yielded a mean tar level of 1.89 milligrams and standard deviation of 0.4 milligrams for a sample of nine cigarettes. Construct a 99% confidence interval for the mean tar content of this brand of cigarette.
4. Researchers claim that the average amount of lean mass that can be put on by an experienced athlete (> 21 yrs old) over the course of a year without performance enhancing drugs is less than 2 pounds. A random sample of 23 experienced athletes followed a strict diet that consisted of 40% protein, 40% carbs, and 20% healthy fats. At the end of one year, the change in lean mass was recorded for each athlete. The mean change was 0.9 lbs. The standard deviation was 0.3 lbs. Express the claim, the null and alternative hypotheses, and find the test statistic that would be used to test the researcher’s claim.
5. A random sample of 2000 voters yielded 530 who reported being in favor of changing the constitution to allow foreign born people to hold the office of President. A 99% confidence interval was constructed for the true proportion of people who are in favor of the change. The resulting interval was as follows: [0.240, 0.290]. If an immigrant group claims that the majority of the public supports the change, does this interval contradict their claim?
8. Shooting ranges need to know the average amount of time that shooters will typically spend on the range to decide whether to charge per hour or to have a single daily rate for unlimited time on the range. For this reason, Texas Shooting Range wants to estimate the mean time that shooters will spend on the range per session if they charge a daily rate for unlimited time on the range. They would like to estimate this mean within 5 minutes and with 98% reliability. If the range’s initial experiences indicate that the standard deviation for the amount of time spent on the range is 22 minutes, how many shooters must be sampled for the range to get the information it desires?
14. A tire manufacturer claims that their tires have a mean lifetime equal to 75,000 miles (assuming regular rotations of the tires are performed). A sample of 36 of their tires are randomly selected and tested. They have a mean lifetime 73,125 miles with a standard deviation of 4,800 miles. Use the p-value method of hypothesis testing to test the company’s claim at the 2% significance level.