Homework 9 Worksheet 1) A sample of 37 registered nurses in Fort Wayne had an average hourly income of $26.52. Suppose that previous research established the population standard deviation of $7.25. Construct a 95% confidence interval for the mean. 2) We wish to estimate the mean serum indirect bilirubin level of 4-day-old infants. The mean for a sample of 16 infants was found to be 5.98 mg/100 cc. Assume that bilirubin levels in 4-day-old infants are approximately normally distributed with a standard deviation of 3.5 mg/100 cc. What is the confidence interval for mean, with 90% confidence? 3) Determine the sample size needed to estimate the mean weight of all second-grade boys if we want to be accurate within 1 lb. with 95% confidence. Assume a normal distribution and that the standard deviation of the boy's weight is 3 lb. 4) For multiple sclerosis patients we wish to estimate the mean age at which the disease was first diagnosed. We want a 90% confidence interval that is 2.5 years wide. If the population standard deviation is 15 years, how large should our sample be? 5) A study was performed that examined free fatty acid concentrations in 38 lean subjects and 31 obese subjects. The lean subjects had a mean level of 299 JEq/L with a standard error of the mean of 30, while the obese subjects had a mean of 744 JEq/L with a standard error of the mean of 62. If it is reasonable to assume that the two populations are normally distributed, what is the 95% confidence interval of the difference in means? 6) A study was conducted to examine the efficacy of oral misoprostol and intravenous oxytocin for labor induction in women with premature rupture of membranes at term. Researchers randomly assigned women to the two treatments. For the 52 women who received oral misoprostol, the mean time in minutes to active labor was 483 minutes. For the 53 women taking oxytocin, the mean time was 358 minutes. If the populations standard deviations are known to be 308 and 144 minutes, respectively. Construct a 99% confidence interval for the difference in mean time to active labor for these two different medications