Question

John davis, a manager of a supermarket, wants to estimate the proportion of customers who use food stamps at his store. he has no initial estimate of what the sample proportion will be. how large a sample is required to estimate the true proportion to within 3 percentage points with 98% confidence?

Answer 1

1509

Explanation:

We know that, formula for number of samples is,

`n= (z^2 * p * q)/(SE^2)`

When nothing is given, we take
`p=0.5` and we know that
`q = 1-p=0.5`.

SE = 0.03 (the true proportion should remain withing 3%)

Putting the values we get,

`n= ((2.33)^2 * 0.5 * 0.5)/((0.03)^2)`

`n= (5.4289 * 0.5 * 0.5)/(0.03 * 0.03) \approx 1509`

Therefore, the sample required to estimate the true proportion to within 3 percentage points is 1509.