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.
-A random sample of 104 light bulbs had a mean life of $\bar { x } = 543$ hours with a standard deviation of $\sigma = 26$ hours. Construct a $90 \%$ confidence interval for the mean life, $\mu$, of all light bulbs of this type.
A) $536 \mathrm { hr }

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.
-A random sample of 104 light bulbs had a mean life of $\bar { x } = 543$ hours with a standard deviation of $\sigma = 26$ hours. Construct a $90 \%$ confidence interval for the mean life, $\mu$, of all light bulbs of this type.
A) $536 \mathrm { hr } < \mu < 550 \mathrm { hr }$
B) $537 \mathrm { hr } < \mu < 549 \mathrm { hr }$
C) $538 \mathrm { hr } < \mu < 548 \mathrm { hr }$
D) $539 \mathrm { hr } < \mu < 547 \mathrm { hr }$

Quizplus · Accepted Answer

The confidence interval is calculated using the formula $\bar{x} \pm z \frac{\sigma}{\sqrt{n}}$. For a 90% confidence level, the z-score is approximately 1.645. Plugging in the values: $543 \pm 1.645 \times \frac{26}{\sqrt{104}}$ gives the interval $539 \mathrm{ hr } < \mu < 547 \mathrm{ hr }$.

Use the Confidence Level and Sample Data to Find a Confidence