Use the confidence level and sample data to find a confidence interval for estimating the population µ.
-Test scores: $\mathrm { n } = 109 , \overline { \mathrm { x } } = 79.1 , \sigma = 6.9 ; 99$ percent
A) $77.4

Question

Use the confidence level and sample data to find a confidence interval for estimating the population µ.
-Test scores: $\mathrm { n } = 109 , \overline { \mathrm { x } } = 79.1 , \sigma = 6.9 ; 99$ percent
A) $77.4 < \mu < 80.8$
B) $78.0 < \mu < 80.2$
C) $77.8 < \mu < 80.4$
D) $77.6 < \mu < 80.6$

Quizplus · Accepted Answer

Given the sample size $n = 109$, sample mean $\overline{x} = 79.1$, population standard deviation $\sigma = 6.9$, and a confidence level of 99%, we use the formula for the confidence interval for the population mean $\mu$ when the population standard deviation is known: $\overline{x} \pm z \frac{\sigma}{\sqrt{n}}$. For a 99% confidence level, the z-value is approximately 2.576. Plugging in the values, we get the confidence interval as $79.1 \pm 2.576 \times \frac{6.9}{\sqrt{109}}$, which calculates to the interval $77.4 < \mu < 80.8$.

Use the Confidence Level and Sample Data to Find a Confidence