Answer:
A sample size of 1380 should be obtained.
Step-by-step explanation:
Minimum sample size:
The minimum sample size is of:
[tex]n = (\frac{z}{E})^2(p_1(1-p_1) + p_2(1-p_2))[/tex]
In which z is the critical value, related to the confidence level, E is the desired margin of error, [tex]p_1[/tex] and [tex]p_2[/tex] are the proportions.
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
Estimates of 22.6% male and 18.1% female from a previous year
This means that [tex]p_1 = 0.226, p_2 = 0.181[/tex].
Within 3 percentage points, minimum sample size:
This is n for which [tex]E = 0.03[/tex]. So
[tex]n = (\frac{z}{E})^2(p_1(1-p_1) + p_2(1-p_2))[/tex]
[tex]n = (\frac{1.96}{0.03})^2(0.226*0.774 + 0.181*0.819)[/tex]
[tex]n = 1379.4[/tex]
Rounding up:
A sample size of 1380 should be obtained.
