Question

A simple random sample of 30 items resulted in a sample mean of 25. The population standard deviation is 7 . 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 =    =7

Sample size n =30

standard error=( /√n) =( 7 /√30) =1.2780

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 * ( 7 / √30 )

E= 2.5049