Use the confidence level and sample data to find a confidence interval for estimating the population µ.
-A laboratory tested 90 chicken eggs and found that the mean amount of cholesterol was 230 milligrams with $\sigma = 16.0$ milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content, $\mu$, of all such eggs.
A) $227

Question

Use the confidence level and sample data to find a confidence interval for estimating the population µ.
-A laboratory tested 90 chicken eggs and found that the mean amount of cholesterol was 230 milligrams with $\sigma = 16.0$ milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content, $\mu$, of all such eggs.
A) $227 < \mu < 233$
B) $226 < \mu < 232$
C) $228 < \mu < 234$
D) $226 < \mu < 233$

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population mean when the population standard deviation is known, we use the formula: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. For a 95% confidence level, the Z-score is approximately 1.96. Plugging in the given values: $230 \pm 1.96 \frac{16}{\sqrt{90}}$, we get the interval $227 < \mu < 233$.

Use the Confidence Level and Sample Data to Find a Confidence