Question

A university dean wishes to estimate the average number of hours that freshmen study each week. The standard deviation from a previous study is a good indication that you can use 2.6 hours as the population standard deviation. How large a sample must be selected if the dean wants to be 96% confident of finding whether the true mean is within 45 minutes of the population mean?

Answer 1

Solution

standard deviation =s =   =2.6 =156 minutes

Margin of error = E = 45

At 97% confidence level the z is ,

= 1 - 97% = 1 - 0.97 = 0.03

/ 2 = 0.03 / 2 = 0.015

Z/2 = Z0.015 = 2.170

sample size = n = [Z/2* / E] 2

n = ( 2.170*156 / 45 )2

n =56.59

Sample size = n =57 rounded