Answer: If in a prior study, a sample of 200 people showed that 40 traveled overseas last year, then n= 385
If no estimate of the sample proportion is available , then n= 601
Step-by-step explanation:
Let p be the prior population proportion of people who traveled overseas last year.
If p is known, then required sample size = [tex]n=p(1-p)(\dfrac{z^*}{E})^2[/tex]
z-value for 95% confidence = 1.96
E = 0.04 (given)
[tex]p=\dfrac{40}{200}=0.2[/tex]
[tex]n=0.2(1-0.2)(\dfrac{1.96}{0.04})^2=384.16\approx385[/tex]
Required sample size = 385
If p is unknown, then required sample size = [tex]n=0.25(\dfrac{z^*}{E})^2[/tex]
, where E = Margin of error , z* =critical z-value.
z-value for 95% confidence = 1.96
E = 0.04 (given)
So, [tex]n=0.25(\dfrac{1.96}{0.04})^2=600.25\approx601[/tex]
Required sample size = 601.
