Question

You are trying to estimate the average amount a family spends on food during a year. In the past the standard deviation of the amount a family has spent on food during a year has been approximately $900. If you want to be 99% sure that you have estimated average family food expenditures within $50, how many families do you need to survey

Answer 1

The number of families required to be surveyed is 2150

Explanation:

Confidence level - 99%

Half length of the interval = $50

Estimated population standard deviation is $900

The sample size formula for estimating a mean n = (z-multiple * бest / B)^2

Where z-multiple = Corresponding standard score for the given confidence level, бest = Estimated population standard deviation, B = Half length of the interval

The z-multiple at 99% confidence level = 2.576

The required sample size is calculated below

n = [(2.576 * 900) / 50}^2

n = (46.368)^2

n = 2149.991424

n = 2150

Conclusion: The number of families required to be surveyed is 2150.