Question

A simple random sample of 30 items resulted in a sample mean of 25. The population standard deviation is 3. Round your answers to two decimal places.

a. What is the standard error of the mean, ?

b. At 95% confidence, what is the margin of error?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 25

Population standard deviation =    = 3

Sample size = n = 30

a) = / n = 3 / 30 = 0.55

b) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

Margin of error = E = Z/2 *

E = 1.96 * 0.55

E = 1.08