1. A sample of 100 adults showed that their sleep time is 6.73 hours. A common recommendation is that population adults should sleep 7 hours or more each night with a population standard deviation of 1.99 hours. Use a 5% level of significance to test the claim the adult mean amount of sleep is less than 7 hours.
2. Assume that the foot lengths of women are normally distributed with a mean of 9.6 inches and a standard deviation of 0.9 inches. Find the probability that 36 women have foot lengths with a mean greater than 9.9 inches.
3 A sample of 205 baby girls weighed 30.4 hg with a standard deviation of 7.1 hg. Develop a 95% confidence interval to estimate the weights of baby girls.
4. A sample of 15 girls at birth had a mean weight of 30.9 hg with a sample standard deviation of 1.8 hg. Construct a 95% confidence interval to estimate the mean weight of girls.
5. Find the sample size required to estimate the mean IQ of professional musicians. Assume that we want 95% confidence level that the mean from the sample is within 3 IQ points of the true population mean with a population standard deviation 15.
6. A sample of 36 regular Coke shows a sample mean of 12.20 ounces with a sample standard deviation of 0.6 ounces. Use a 5% significant level to test the claim that cans of Coke have a mean volume exactly 12 ounces.
7. A sample of 6 child booster seats for cars showed that the booster seat has a mean of 804 hic (standard head injury condition units) with a standard deviation of 273 hic. Use a 1% significant level to test the claim that the child booster seats are at least 1000 hic to meet the safety standard.
8. A survey of 420095 cell phone users found that 0.0321% of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0340% for those not using cell phones. Use the sample data to construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.
9. Find the sample size required to estimate the percentage or proportion of college students who take a statistics course, if on a prior study, 50% of students surveyed took statistics. Assume that we want 95% confidence level that the percentage or proportion from the sample is within 3% points of the true population proportion.
10. A random sample of 860 births in New York State included 400 boys. Use a 5% level of significance to test the claim that 51.2% of newborn babies are boys.