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.
A) $173.9 \mathrm { mg }

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. 
A) $173.9 \mathrm { mg } < \mu < 196.1 \mathrm { mg }$
B) $173.7 \mathrm { mg } < \mu < 196.3 \mathrm { mg }$
C) $173.8 \mathrm { mg } < \mu < 196.2 \mathrm { mg }$
D) $175.9 \mathrm { mg } < \mu < 194.1 \mathrm { mg }$

Quizplus · Accepted Answer

We use the formula for a confidence interval for the population mean:

$
\bar{X} \pm t_{\alpha/2}\left(\dfrac{s}{\sqrt{n}}ight)
$

where $\bar{X}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, $t_{\alpha/2}$ is the critical value from the t-distribution with $n-1$ degrees of freedom (for a 95% confidence interval and $n-1=11$, $t_{\alpha/2}=2.201$).

Plugging in the given values, we get:

$
185 \pm 2.201 \left(\dfrac{17.6}{\sqrt{12}}ight) \
185 \pm 12.099 \
\Rightarrow 	ext{CI: } (173.9, 196.1)
$

Therefore, the best choice is C.

Use the Given Degree of Confidence and Sample Data to Construct