I took a large sample of households in a city, and based on that, estimate the standard deviation of the income for all households in the city is $800. In order to make a desired conclusion about the income for all the households in the city, I want the sample mean for another sample to have a standard deviation of no more than $100. How many households must I have in this new sample?
A. 100
B. 8
C. 64
64
To find out how many households you must have in the new sample, we can use the formula for the standard error of the mean, which is the standard deviation divided by the square root of the sample size.
In this case, you want the sample mean to have a standard deviation of no more than $100. So, we can set up the following inequality:
Standard Error of the Mean ≤ Desired Standard Deviation
σ/sqrt(n) ≤ 100
Since you know that the estimated standard deviation of the income for all households in the city is $800, you can substitute the value into the equation:
$800/sqrt(n) ≤ 100
Now, we can solve for the minimum sample size 'n' by rearranging the equation:
sqrt(n) ≥ $800 / $100
sqrt(n) ≥ 8
n ≥ 8^2
n ≥ 64
Therefore, you must have at least 64 households in the new sample to ensure that the sample mean has a standard deviation of no more than $100.
The correct answer is C. 64.