1. Given that: Point estimate, X = 4 hours. Standard deviation of the sample mean = 0.2551 Find the confidence interval for the 95% confidence interval. 2. A statistician chooses 27 randomly selected dates, and when examining the occupancy records of a particular motel for those dates, find a mean 28 and standard deviation of 5.86 rooms rented. Find the 99% confidence interval. 3. A random sample of 225 1st year statistics tutorials was selected from the past 5 years and the number of students absent from each one recorded. The results were X=1.6 and s = 270. Estimate the mean number of absences per tutorial over the past 5 years with 90% confidence. 4. Some studies of Alzheimer's disease (AD) have shown an increase in 14CO2 production in patients with the disease. In one such study the following 14CO2 values were obtained from 16 neocortical biopsy samples from AD patients. 1009 1280 1180 1255 1547 2352 1956 1080 1776 1767 1680 2050 1452 2857 3100 1621 Assume that the population of such values is normally distributed with a standard deviation of 350. Find the 95% confidence interval. 5. 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. Develop the 90% confidence interval