Question

A simple random sample of 40 items resulted in a sample mean of 10. The population standard deviation is = 6. 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:

Sample size =n = 40

Sample mean =

Population standard deviation =

Part a) What is the standard error of the mean ?

Thus the standard error of the mean is :

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

the margin of error is given by:

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Thus at 95% confidence, the margin of error =