Question

Determine the margin of error for a 99​% confidence interval to estimate the population mean when s​ = 40 for the sample sizes below. ​a) nequals12 ​b) nequals25 ​c) nequals50

​a) The margin of error for a 99​% confidence interval when nequals12 is _____. ​(Round to two decimal places as​ needed.) ​

b) The margin of error for a 99​% confidence interval when nequals25 is ____. ​(Round to two decimal places as​ needed.) ​

c) The margin of error for a 99​% confidence interval when nequals50 is ____ ​(Round to two decimal places as​ needed.)

Answer 1

Margin of error when population standard deviation () is unknown and sample size(n) is small

Margin of error for large sample

a) n=12, s=40

t value at 99% confidence interval with 11 (n-1=12-1) degrees of freedom= 3.1058

=35.85

b) n=25

t value at 99% confidence interval with 24  degrees of freedom= 2.7969

= 22.38

c) n=50

z value for 99% confidence interval = 2.5758

= 14.57