Answer:
1509
Step-by-step explanation:
We know that, formula for number of samples is,
[tex]n= \frac{z^2 \times p \times q}{SE^2}[/tex]
When nothing is given, we take [tex]p=0.5[/tex] and we know that [tex]q = 1-p=0.5[/tex].
SE = 0.03 (the true proportion should remain withing 3%)
Putting the values we get,
[tex]n= \frac{(2.33)^2 \times 0.5 \times 0.5}{(0.03)^2}[/tex]
[tex]n= \frac{5.4289 \times 0.5 \times 0.5}{0.03 \times 0.03} \approx 1509[/tex]
Therefore, the sample required to estimate the true proportion to within 3 percentage points is 1509.
