A professor at a university wants to estimate the average nu

A professor at a university wants to estimate the average number of hours of sleep the students get during exam week. The professor wants to find a sample mean that is within 4.266 hours of the true average for all college students at the university with 99% confidence. If the professor knows the standard deviation of the sleep times for all college students is 2.539, what sample size will need to be taken?

A. 2

B. 13

C. We do not have enough information to answer this question since we were not given the sample mean.

D. 8

E. 3

Solution

Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.01% LOS is = 2.58 ( From Standard Normal Table )
Standard Deviation ( S.D) = 2.359
ME =4.266
n = ( 2.58*2.359/4.266) ^2
= (6.086/4.266 ) ^2
= 2.035 ~ 3