1. In order to identify baby growth patterns that are unusual, we need to construct a confidence interval estimate of the mean head circumference of all babies that are 2 months old. A random sample of 100 babies is obtained and the mean head circumference is found to 40.6cm. Assuming that the population standard deviation is known to be 1.6 cm. Find a 95% confidence interval estimate for the mean head circumference of all two-moth old babies. What aspect of this problem is not realistic?
2. A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution which appears to be symmetric and bell-shaped with a mean of $9004 and a standard deviation of $5629 based on data from the U. S. Department of Transportation. Construct a 99% confidence interval for the mean of all such costs.
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.
3. According to the National Institute for Occupational Safety and Health, job stress poses a major threat to the health of workers. A national survey of restaurant employees found that 75% said that job stress had a negative impact on their personal lives. A sample of 100 employees of a restaurant chain finds that 68 answer "Yes" when asked: "Does job stress have a negative impact on your personal life?" Is this good reason to think that the proportion of all employees of this chain who would say "Yes" differs from the national proportion? Use a 5% level of significance.
4. The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 182.9lbs. Assuming that the population standard deviation is known to be 121.8lbs, use a 0.05 level of significance to test the claim the population mean of all such bear weights is less than 200lbs.
5. The birth weights (in kilograms) are recorded for a sample of male babies born to mothers taking a special vitamin supplement (based on data from the New York Department of Health). When testing the claim that the mean birth weight for all male babies of mothers given vitamins is equal to 3.39kg, which is the mean weight of the population of all male babies, a sample of 16 babies had a mean of 3.675kg and a standard deviation of 0.657. Based on these results, does the vitamin supplement appear to have any effect on the mean birth weight? Use the 0.01 level of significance.