Solve the problem. Round your answer to the nearest whole number unless indicated otherwise.
-An economist wants to estimate mean annual income for recent college graduates majoring in statistics. how many such incomes must be found if he wants to be 95% confident that the sample mean is within $500 of the true population mean? Assume that a previous study has revealed that for such incomes $\sigma = \$ 5250$
A)441
B)10,500
C)470
D)21

Question

Quizplus · Accepted Answer

To determine the sample size needed, use the formula for the sample size in estimating a mean: $n = \left(\frac{Z\sigma}{E}\right)^2$, where $Z$ is the Z-value corresponding to the desired confidence level (for 95% confidence, $Z = 1.96$), $\sigma$ is the population standard deviation (\$5250), and $E$ is the margin of error (\$500). Plugging in the values: $n = \left(\frac{1.96 \times 5250}{500}\right)^2 \approx 441$.

Solve the Problem σ=$5250\sigma = \$ 5250σ=$5250 A)441 B)10,500 C)470 D)21

Solve the Problem $\sigma = \$ 5250$ A)441
B)10,500
C)470
D)21