Solve the problem. Round your answer to the nearest whole number unless indicated otherwise.
-A government survey conducted to estimate the mean price of houses in a metropolitan area is designed to have a margin of error of $10,000. Pilot studies suggest that the population standard deviation is $40,000. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.
A)4096
B)64
C)32
D)8

Question

Quizplus · Accepted Answer

The sample size can be calculated using the formula for margin of error: $ E = \frac{z \cdot \sigma}{\sqrt{n}} $. Solving for $ n $ gives $ n = \left(\frac{z \cdot \sigma}{E}\right)^2 $. Assuming a 95% confidence level, $ z \approx 1.96 $. Plugging in the values: $ n = \left(\frac{1.96 \cdot 40000}{10000}\right)^2 = 64 $.

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