Choose the one alternative that best completes the statement or answers the question.
-A group of 40 car owners calculated that their average repair bill was $\$ 192$ with a population standard deviation of $\$ 8$. Compute the $95 \%$ confidence interval for the mean repair bill of all the owners.
A) $( \$ 189.50 , \$ 194.50 )$
B) $( \$ 186.50 , \$ 197.50 )$
C) $( \$ 188.50 , \$ 195.60 )$
D) $( \$ 187.30 , \$ 196.10 )$

Question

Quizplus · Accepted Answer

The $95\%$ confidence interval for the mean is calculated using the formula $\bar{x} \pm z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level (for $95\%$, $z = 1.96$), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $192 \pm 1.96 \times \frac{8}{\sqrt{40}}$ results in the interval $(\$189.50, \$194.50)$.

Choose the One Alternative That Best Completes the Statement or Answers