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 TIE students and records their weekday mean sleep time as $.30 hours. Assume that the population standard deviation is fairly stable at 1.60 hours. {a} Construct a 95% confidence interval for the population mean weekday sleep time of all students of this college. Use the following table of a; for most common cc values. nmammm-mmm mmmm-\"mm Emma-\"mm Find 2; = C] Round the margin of error and condence interval values to 2 decimal places. Calculate the margin of error E = C] What is the 9E3? confidence interval? DEPEC] {b} If the researcher wants to he was confident that the sample mean is within 1115 hours [or 15 min} of the true population mean weekday sleep time, how many students should he include in the sample? Find as = C] 3 Round your answer [11} UP to the next whole number. The required sample size n is :]