Question

A laboratory tested 12 chicken eggs and found that the mean amount of cholesterol was 183 milligrams with s=12.7. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs and demonstrate two methods for finding margin of error.

Answer 1

Population standard deviation is unknown, so we will use t distribution instead of z distribution.  

First, we need to find the t critical value for 95% confidence interval

degree of freedom = n-1 = 12-1= 11

using t distribution table for two tailed hypothesis with df = 11, we get

t critical = 2.20

Formula for confidence interval is given as

CI =

where we have x(bar) = 183, s=12.7, n=12 and t = 2.20

setting the values, we get

CI =

So, this is the required 95% confidence interval

Two methods for finding the margin of error

(1) we know that margin of error is equal to half of the length of confidence interval

So, margin of error = (upper limit - lower limit)/2 = (191.066 - 174.934)/2 = 16.132/2 = 8.066

Margin of error is 8.066

(2) We know the formula for margin of error is given as

ME =

where t = 2.20, s = 12.7 and n = 12

setting the values, we get

ME =

So, margin of error is 8.066