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. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
A) $173.7 \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. Construct a  95% confidence interval for the true mean cholesterol content of all such eggs.
A) $173.7 \mathrm { mg } < \mu < 196.3 \mathrm { mg }$
B) $175.9 \mathrm { mg } < \mu < 194.1 \mathrm { mg }$
C) $173.8 \mathrm { mg } < \mu < 196.2 \mathrm { mg }$
D) $173.9 \mathrm { mg } < \mu < 196.1 \mathrm { mg }$

Quizplus · Accepted Answer

The confidence interval is calculated using the formula: $\bar{x} \pm t^* \frac{s}{\sqrt{n}}$, where $\bar{x} = 185$, $s = 17.6$, $n = 12$, and $t^*$ is the t-value for 95% confidence with 11 degrees of freedom. The correct interval is $173.8 \mathrm { mg } < \mu < 196.2 \mathrm { mg }$.

Use the Given Degree of Confidence and Sample Data to Construct