A researcher wishes to estimate the mean amount of money spent per month on food by households in a certain neighborhood. She desires a margin of error of $30. Past studies suggest that a population standard deviation of $248 is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.
A. 274
B. 284
C. 264
D. 272
C
To estimate the minimum sample size needed to estimate the population mean with a desired accuracy, we can use the formula:
n = (z * σ / E)²
Where:
n = sample size
z = Z-score corresponding to the desired level of confidence (e.g., 1.96 for a 95% confidence level)
σ = population standard deviation
E = desired margin of error
In this case, the researcher desires a margin of error of $30 and past studies suggest a population standard deviation of $248. Therefore,
n = (1.96 * 248 / 30)²
Calculating this expression, we get:
n ≈ 264.6896
Since we cannot have a fractional number of samples, we need to round up to the nearest whole number. So, the minimum sample size needed is 265.
Among the given answer choices, the closest option to 265 is C. So, the correct answer is C.