Question

A laboratory tested 86 chicken eggs and found that the mean amount of cholesterol was 18.2 milligrams with s = 18.2 milligrams. Find the 95% confidence interval. Round to the nearest whole number.

Answer 1

Take into account that the confidence interval is given by:

`\mu\pm Z\cdot\frac{s}{\sqrt[]{n}}`

where

μ: mean = 18.2

Z: z-value for 95% confidence = 1.96

s = 18.2

n: sample = 86

Replace the previous values into the confidence interval formula:

`\begin{gathered} 18.2+1.96\cdot\frac{18.2}{\sqrt[]{86}} \\ 18.2\pm3.85 \end{gathered}`

Hence, the confidence interval is:

CI = (18.2 - 3.85 , 18.2 + 3.85) = (14.35 , 22.05)

Rounded to the nearest whole number the confidence interval is:

CI = (14 , 22)