Question

A lab tested 99 chicken eggs and found that the average amount of cholesterol was 217 milligrams, sd= 20 milligrams. construct a 97% confidence interval for the true mean cholesterol content, u, of all those eggs

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 217

Population standard deviation =    = 20

Sample size = n = 99

At 97% confidence level

= 1 - 97%  

= 1 - 0.97 =0.03

/2 = 0.015

Z/2 = Z_{0.015 =} 2.17

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

= 2.17 * ( 20 /  99 )

= 4.36

At 97% confidence interval estimate of the population mean is,

  ± E

217 ± 4.36   

( 212.64, 221.36 )