Question

Suppose you have a sample of size 30 with a mean of 48 and a population standard deviation of 13.1. What is the maximal margin of error associated with a 95% confidence interval for the true population mean?

In your calculations, use z = 2.

Give your answer as a decimal, to two places

m =  ounces

Answer 1

Solution =

Given,

= 48   

= 13.1   

n = 30   

Note that, Population standard deviation() is known..So we use z distribution.

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96 = 2

The margin of error is given by

E =  /2 * ( / n )

= 2 * ( 13.1/ 30 )

= 4.78

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

( 48 - 4.78 )   <   <  ( 48 + 4.78 )

43.22 <   < 52.78

Required 95% confidence interval is ( 43.22 , 52.78 )