A researcher wishes to estimate the average annual expenditures per household on gasoline. The estimate must be accurate within plus or minus $100 and the estimated standard deviation in such expenditures is $500.
Use this problem to answer the following two questions.
-For a 95% confidence interval (use z=2), the required sample size is

Question

Quizplus · Accepted Answer

The formula for determining sample size for estimating a mean with a specified margin of error (E) at a certain confidence level is $n = \left(\frac{z \cdot \sigma}{E}\right)^2$. Given $z = 2$, $\sigma = 500$, and $E = 100$, substituting these values gives $n = \left(\frac{2 \cdot 500}{100}\right)^2 = \left(\frac{1000}{100}\right)^2 = 10^2 = 100$.

A Researcher Wishes to Estimate the Average Annual Expenditures Per