Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$. 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. A confidence interval of $173.8 \mathrm { mg }

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$. 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. A confidence interval of $173.8 \mathrm { mg } < \mu < 196.2 \mathrm { mg }$ is constructed for the true mean cholesterol content of all such eggs. It was assumed that the population has a normal distribution. What confidence level does this interval represent?
A) $99 \%$
B) $95 \%$
C) $98 \%$
D) $80 \%$

Quizplus · Accepted Answer

The confidence interval is calculated using the sample mean, standard deviation, and the t-distribution. Given the interval $173.8 \mathrm { mg } < \mu < 196.2 \mathrm { mg }$ and the sample mean of 185 mg, the margin of error is 11.2 mg. Using the t-distribution for 11 degrees of freedom (n-1) and the given margin of error, the confidence level that matches this interval is $95\%$.

Use the Given Degree of Confidence and Sample Data to Construct