Solve the problem.
-A sample of 35 washing machines yields a mean replacement time of 9.0 years. Assuming that $\sigma$ = 2.4 years, find the margin of error in estimating $\mu$ at the 90% level of confidence.
A)0.7 years
B)0.5 years
C)2.5 years
D)0.1 years

Question

Solve the problem.
-A sample of 35 washing machines yields a mean replacement time of 9.0 years. Assuming that $\sigma$ = 2.4 years, find the margin of error in estimating $\mu$ at the 90% level of confidence. 
A)0.7 years
B)0.5 years
C)2.5 years
D)0.1 years

Quizplus · Accepted Answer

The margin of error (E) for estimating the mean ($\mu$) with a certain level of confidence is given by the formula $E = Z \cdot \frac{\sigma}{\sqrt{n}}$, where $Z$ is the Z-score corresponding to the desired level of confidence, $\sigma$ is the population standard deviation, and $n$ is the sample size. For a 90% confidence level, the Z-score is approximately 1.645. Given $\sigma = 2.4$ years and $n = 35$, we calculate $E = 1.645 \cdot \frac{2.4}{\sqrt{35}} \approx 0.7$ years.

Solve the Problem σ\sigmaσ = 24 Years, Find the Margin of Error in Estimating

Solve the Problem $\sigma$ = 24 Years, Find the Margin of Error in Estimating