Question

A simple random sample of 30 items resulted in a sample mean of 10. The population standard deviation is σ = 9. Round your answers to two decimal places. 

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

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

Answer 1

Solution :

Given that,

Population standard deviation =    =9

Sample size n =30

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   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 9 / 30)

=3.22