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)`

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)(\sigma)/(√(n))\\\\=190\pm(1.96)(11.7)/(√(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.