Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s=17.6 milligrams. Construct a​ 95% confidence interval for the true mean cholesterol content of all such eggs.

A.173.7mg <μ <196.3mg

B.173.8mg <μ <196.2mg

C.175.9mg <μ <194.1mg

D.173.9mg <μ <196.1mg

Answer 1

Solution :

Given that,

t /2,df = 2.201

Margin of error = E = t/2,df * (s /n)

= 2.201 * (17.6 / 12)

Margin of error = E = 11.2

The 95% confidence interval estimate of the population mean is,

- E < < + E

185 - 11.2 < < 185 + 11.2

173.8 < < 196.2

173.8mg <μ <196.2mg

option B. is correct