Question

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 182 milligrams with a standard deviation of 15.4 milligrams.  Construct a 99% confidence interval for the true mean cholesterol content of all such eggs. Write a sentence summarizing your results.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 182

Population standard deviation =    = 15.4

Sample size = n = 12

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 15.4 /  12 )

= 11.45

At 99% confidence interval estimate of the population mean is,

   - E < <   + E

182 - 11.45 <   < 182 + 11.45

170.55 <   < 193.45

( 170.55 , 193.45 )

At 99% confidence interval estimate of the population mean is  ( 170.55 , 193.45 )