A simple random sample of 40 items resulted in a sample mean

A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is 5.

a. What is the standard error of the mean (to 2 decimals)?

b. At 95% confidence, what is the margin of error (to 2 decimals)?

Solution

Sample Mean = 25
SD = 5
Sample Size (n) = 40
Standard Error (SE) = SD/root(n) = 0.79
alpha (a) = 1 - 0.95 = 0.05

z critical value for 95% confidence interval:
z(a/2) = z(0.025) = 1.96

Margin of Error (ME) = z(a/2) x SE = 1.55

95% confidence interval is given by:
Sample Mean +/- (Margin of Error) = 25 +/- 1.55
= (23.45 , 26.55)