A laboratory tested 60 chicken eggs and found that the mean amount of cholesterol was 241 milligrams with s = 14.7 milligrams.Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
A)(237.3,244.7)
B)(231.5,248.6)
C)(231.7,250.3)
D)(233.4,248.6)
E)(231.7,250.5)

Question

Quizplus · Accepted Answer

To construct the confidence interval, we can use the formula:

CI = x̄ ± t*(s/√n)

where x̄ is the sample mean (241), s is the sample standard deviation (14.7), n is the sample size (60), and t is the t-value corresponding to a 95% confidence level with 59 degrees of freedom (since n-1 = 59).

Using a t-table or calculator, we can find that the t-value is approximately 2.002. Substituting these values into the formula, we get:

CI = 241 ± 2.002*(14.7/√60)
CI = (237.3,244.7)

Therefore, the best choice is A) (237.3,244.7) as it is the correct confidence interval for the true mean cholesterol content of all such eggs with a 95% confidence level.

A Laboratory Tested 60 Chicken Eggs and Found That the Mean