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 sample size. 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=12-1=11), this margin of error corresponds to a 95% confidence level.

Use the Given Degree of Confidence and Sample Data to Construct