Question

You are doing research on how much sleep students get who are in a Master's degree program. You randomly select 300 students and determine what the mean number of hours they slept was 5.5 hours, with a standard deviation of .50 hours. What are the upper and lower confidence limits at the 95 percent confidence level?

Answer 1

Solution :

Given that,

= 5.5

= 0.50

n = 300

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * ( 0.50/ 300)

= 0.0566

At 95% confidence interval estimate of the population mean is,

- E < < + E

5.5 - 0.0566 < <5.5 + 0.0566

5.4434< < 5.5566

lower limit = 5.4434

upper limit = 5.5566