Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your answer to the same number of decimal places as the sample mean.
-Test scores: $\mathrm { n } = 102 , \overline { \mathrm { x } } = 77.4 , \sigma = 6.5 ; 99 \%$ confidence
A) $76.1

Question

Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your answer to the same number of decimal places as the sample mean.
-Test scores: $\mathrm { n } = 102 , \overline { \mathrm { x } } = 77.4 , \sigma = 6.5 ; 99 \%$ confidence
A) $76.1 < \mu < 78.7$
B) $75.7 < \mu < 79.1$
C) $75.9 < \mu < 78.9$
D) $76.3 < \mu < 78.5$

Quizplus · Accepted Answer

The 99% confidence interval is calculated using the formula $\overline{x} \pm z \left(\frac{\sigma}{\sqrt{n}}\right)$. For 99% confidence, $z$ is approximately 2.576. Plugging in the values, the interval is $77.4 \pm 2.576 \left(\frac{6.5}{\sqrt{102}}\right)$, which rounds to $75.7 < \mu < 79.1$.

Use the Confidence Level and Sample Data to Find a Confidence