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.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 185

sample standard deviation = s = 17.6

sample size = n = 12

Degrees of freedom = df = n - 1 = 12 - 1 = 11

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,11 = 2.201

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

= 2.201 * (17.6 / 12)

= 11.2

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

- E < < + E

185 - 11.2 < < 185 + 11.2

173.8 < < 196.2

(173.8 , 196.2)