Question

Find the confidence interval specified. Assume that the population is normally distributed.A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 206 milligrams with s = 12.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

Answer 1

Answer: 206 ± 8.069

Step-by-step explanation: Since the confidence interval is 95%, α = 0.025.

mean = 206

s = 12.7

standard error (SE) = $\frac{12.7}{\sqrt{12} }$

SE = 3.66

The population is small, so use t-score. To do so, the degrees of freedom is:

n - 1 = 11

α = 0.025

Looking the t-score table for line 11 and column 0.025:

t-score = 2.201

Confidence interval will be:

mean ± t*SE

206 ± 2.201*3.66

206 ± 8.069

The confidence interval for the true mean is 206 ± 8.069