In: Statistics and Probability
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?
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 = Z0.025 = 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