Some latest study shows that college students are increasingly skimping on their sleep. A researcher from a small community college wants to estimate the mean weekdays sleep time of its students. He takes a random sample of 85 students and records their weekday mean sleep time as 6.10 hours. Assume that the population standard deviation is fairly stable at 1.70 hours. (a) Construct a 96% confidence interval for the population mean weekday sleep time of all students of this college. Use the following table of za for most common a values. a 0.005 0.01 0.02 0.03 0.04 0.05 0.06 0.1 Za 2.575 2.33 2.05 1.88 1.75 1.645 1.555 1.28 Za 2.81 2.575 2.33 2.17 2.05 1.96 1.88 1.645 Find z Round the margin of error and the confidence interval endpoints to 2 decimal places. Calculate the margin of error E = What is the 96% confidence interval? (b) If the researcher wants to be 99% confident that the sample mean is within 0.25 hours (or 15 min) of the true population mean weekday sleep time, how many students should he include in the sample? Find za = Round your answer (n) UP to the next whole number. The required sample size n is