Question

Determine the smallest sample size required to estimate the population mean under the given specifications in parts a through d below.

a. e=2.6​, confidence level=90​%, data between 70 and 150

The smallest sample size required to estimate the population mean is . ​(Round up to the nearest whole number as​ needed.)

Answer 1

Solution:

First we estimate the value of the standard deviation using range rule of thumb.

= Range/4 = (largest observation - smallest observation)/4 = (150 - 70)/4 = 20

Now , also given margin of error E = 2.6

confidence level c = 90% = 0.90

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.05 and 1- /2 = 0.950

Search the probability 0.950 in the Z table and see corresponding z value

= 1.645

Now, sample size (n) is given by,

=  {(1.645 * 20 )/ 2.6 }²

= 160.1198

= 161 ..(round to the next whole number)

The smallest sample size required to estimate the population mean is 161.