Question

A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with σ=19.0 milligrams. Construct a​ 95% confidence interval for the true mean cholesterol​ content, μ​, of all such eggs.

A. 223mg <μ <232mg

B.225mg <μ <233mg

C.224mg <μ<232mg

D.223mg <μ <231mg

Answer 1

Solution :

Given that,

Point estimate = sample mean =     =228

Population standard deviation =    = 19.0

Sample size n =82

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 * (19.0 / 82 )

E= 4.1125
At 95% confidence interval estimate of the population mean
is,

- E < < + E

228 - 4.1125 <   < 228+ 4.1125

224 <   < 232