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 σ = $1200. If you want to be 99% sure that you have estimated average family food expenditures within $60, how many families do you need to survey?

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amcool amcool · Answer 1 · 2022-09-06T19:23:33+02:00

Based on the calculation below, the number of families that has to be surveyed is 2,654.

From the question, we have:

SD = population standard deviation = $1200

Confidence level = 99%

A = Average or half length of the interval = $60

Also, we have:

z-multiple at 99% confidence level = 2.576

The sample size or the number of families that has to be surveyed can be calculated using the following formula:

Number of families to survey or sample size =

Number of families to survey or sample size = ((z-multiple * SD) / A)^2 ....................... (1)

Substituting all the values into equation (1), we have:

Number of families to survey or sample size = ((2.576 * 1200) / 60)^2 = 51.52^2 = 2,654.3104 = 2,654

Learn about the sample size here: https://brainly.com/question/24158610.

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