Find the confidence interval specified.
-A sample of 38 people were randomly selected from among the workers in a shoe factory. The time taken for each person to polish a finished shoe was measured. The sample mean was 4.0 minutes.
Assume that $\sigma =$ 0.71 minutes. Construct a 90% confidence interval for the true mean time, $\mu$ to Polish a shoe.
A)3.70 to 4.30 minutes
B)3.81 to 4.19 minutes
C)3.73 to 4.27 minutes
D)3.77 to 4.23 minutes

Question

Find the confidence interval specified.
-A sample of 38 people were randomly selected from among the workers in a shoe factory. The time taken for each person to polish a finished shoe was measured. The sample mean was 4.0 minutes.
Assume that $\sigma =$ 0.71 minutes. Construct a 90% confidence interval for the true mean time, $\mu$ to Polish a shoe. 
A)3.70 to 4.30 minutes
B)3.81 to 4.19 minutes
C)3.73 to 4.27 minutes
D)3.77 to 4.23 minutes

Quizplus · Accepted Answer

The confidence interval is calculated using the formula for a Z-interval since the population standard deviation ($\sigma$) is known. The formula is $\bar{x} \pm Z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the desired confidence level (for 90% confidence, $Z \approx 1.645$), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values ($\bar{x} = 4.0$, $\sigma = 0.71$, $n = 38$), we find the margin of error and then the confidence interval, which matches choice B.

Find the Confidence Interval Specified σ=\sigma =σ= 071 Minutes μ\muμ To Polish a Shoe

Find the Confidence Interval Specified $\sigma =$ 071 Minutes $\mu$ To Polish a Shoe