Solve the problem.
-A sample of 71 college students yields a mean annual income of $\$ 3595$. Assuming that $\sigma = \$ 898$, find the margin of error in estimating $\mu$ at the $99 \%$ level of confidence.
A)$\$ 248$
B) $\$ 1099$
C) $\$ 274$
D) $\$ 209$

Question

Solve the problem.
-A sample of 71 college students yields a mean annual income of $\$ 3595$. Assuming that $\sigma = \$ 898$, find the margin of error in estimating $\mu$ at the $99 \%$ level of confidence.  
A)$\$ 248$
B) $\$ 1099$
C) $\$ 274$
D) $\$ 209$

Quizplus · Accepted Answer

The margin of error (E) for estimating the mean ($\mu$) with a known standard deviation ($\sigma$) at a certain confidence level is given by $E = Z \cdot \frac{\sigma}{\sqrt{n}}$, where $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. For a 99% confidence level, the Z-score is approximately 2.576. Plugging in the values: $E = 2.576 \cdot \frac{898}{\sqrt{71}} \approx 274$.

Solve the Problem $3595\$ 3595$3595 Assuming That σ=$898\sigma = \$ 898σ=$898

Solve the Problem $\$ 3595$ Assuming That $\sigma = \$ 898$