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 80 students and records their weekday mean sleep time as 6.10 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 z2 for most commonvalues.

	0.005	0.01	0.02	0.03	0.04	0.05	0.06	0.1
z	2.575	2.33	2.05	1.88	1.75	1.645	1.555	1.28
z2	2.81	2.575	2.33	2.17	2.05	1.96	1.88	1.645

Find z2=

Round the margin of error and the confidence interval endpoints to 2 decimal places.

Calculate the margin of errorE=

What is the 95% confidence interval? ans: ____<< ____

(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 z2=

Round your answer (n) UP to the next whole number.

The required sample sizen is