Question

A 99% confidence interval for a population mean was reported to be 154 to 158. If 15, what sample size was used in this study? (Round your answer to next whole number.)

Answer 1

Solution:

A 99% confidence interval for a population mean was reported to be 154 to 158.

Lower limit = 154

Upper limit = 158

Margin of error = (Upper - Lower)2 = (158 -154)/2

E = 2

Given that population SD is 15

= 15

For 99% confidence ,

c = 0.99

= 1- c = 1- 0.99 = 0.01

  /2 = 0.01 2 = 0.005 and 1- /2 = 0.995

Search the probability 0.995 in the Z table and see corresponding z value

= 2.576   

Now, sample size (n) is given by,

= {(2.576 * 15)/ 2 }²

=  374

Answer : 374

=     ..(round to the next whole number)