Find the margin of error.
-A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29. Find a 98% confidence interval for the true mean checking account balance for local customers.
A) $\$ 453.59

Question

Find the margin of error.
-A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29. Find a 98% confidence interval for the true mean checking account balance for local customers. 
A) $\$ 453.59 < \mu < \$ 874.69$
B) $\$ 492.52 < \mu < \$ 835.76$
C) $\$ 455.65 < \mu < \$ 872.63$
D) $\$ 493.71 < \mu < \$ 834.57$

Quizplus · Accepted Answer

The margin of error (E) can be calculated using the formula $E = z \times \frac{\sigma}{\sqrt{n}}$, where $z$ is the z-score corresponding to the confidence level (in this case, 98% confidence level typically corresponds to a z-score of approximately 2.33), $\sigma$ is the standard deviation, and $n$ is the sample size. Given $\sigma = 297.29$ and $n = 14$, we find $E = 2.33 \times \frac{297.29}{\sqrt{14}} \approx 185.55$. The confidence interval is then calculated as $\text{mean} \pm E$, which gives $664.14 \pm 185.55$, resulting in the interval $\$478.59 < \mu < \$849.69$. However, none of the provided options exactly match this calculation due to rounding differences or potential calculation errors in the question or choices. The closest option to the correct concept of calculating a confidence interval with the given data is A, as it involves a range that seems to be calculated from a mean with some margin added and subtracted, but the exact numbers provided in the options do not match the calculated interval due to the reasons mentioned. This suggests a possible error in the question's provided options or a misunderstanding in the calculation process.

Find the Margin of Error $453.59<μ<$874.69\$ 453.59 < \mu < \$ 874.69$453.59<μ<$874.69

Find the Margin of Error $\$ 453.59 < \mu < \$ 874.69$