Question

A laboratory tested 85 chicken eggs and found that the mean amount of cholesterol was 190 milligrams. Assume that the sample standard deviation is 11.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs. State your conclusion in a statistical sentence.

Answer 1

Answer:   $(182.356,\ 197.644)$

Step-by-step explanation:

Given : Significance level : $\alpha:1-0.95=0.05$

Sample size : n=85

Critical value : $z_{\alpha/2}=1.96$

Sample mean : $\overline{x}=190$

Standard deviation : $\sigma=11.7$

The confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=190\pm(1.96)\dfrac{11.7}{\sqrt{9}}\\\\=190\pm7.644\\\\=(190-7.644,\ 190+7.644)=(182.356,\ 197.644)$

Thus, the 95% confidence interval for the true mean cholesterol content, μ, of all such eggs = $(182.356,\ 197.644)$

Hence, we conclude that the true population mean of amount of cholesterol lies between 182.356 and 197.644.