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 108 light bulbs had a mean life of $\bar { x } = 547$ hours with a standard deviation of $\sigma = 36$ hours. Construct a $90 \%$ confidence interval for the mean life, $\mu$, of all light bulbs of this type.
A) $541 \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 108 light bulbs had a mean life of $\bar { x } = 547$ hours with a standard deviation of $\sigma = 36$ hours. Construct a $90 \%$ confidence interval for the mean life, $\mu$, of all light bulbs of this type.
A) $541 \mathrm { hr } < \mu < 553 \mathrm { hr }$
B) $538 \mathrm { hr } < \mu < 556 \mathrm { hr }$
C) $539 \mathrm { hr } < \mu < 555 \mathrm { hr }$
D) $540 \mathrm { hr } < \mu < 554 \mathrm { hr }$

Quizplus · Accepted Answer

The correct answer is A because the confidence interval is calculated as $\bar { x } \pm z_{\alpha/2} \frac { \sigma } { \sqrt { n } }$, where $\bar { x }$ is the sample mean, $z_{\alpha/2}$ is the critical value from the standard normal distribution corresponding to the desired confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. For a $90 \%$ confidence level, $z_{\alpha/2} = 1.645$. Plugging in the given values, we get $547 \pm 1.645 \frac { 36 } { \sqrt { 108 } } = 547 \pm 6$. Therefore, the $90 \%$ confidence interval is $541 \mathrm { hr } < \mu < 553 \mathrm { hr }$.

Use the Confidence Level and Sample Data to Find a Confidence