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 = ![n=p(1-p)(\dfrac{z^*}{E})^2](https://tex.z-dn.net/?f=n%3Dp%281-p%29%28%5Cdfrac%7Bz%5E%2A%7D%7BE%7D%29%5E2)
z-value for 95% confidence = 1.96
E = 0.04 (given)
![p=\dfrac{40}{200}=0.2](https://tex.z-dn.net/?f=p%3D%5Cdfrac%7B40%7D%7B200%7D%3D0.2)
![n=0.2(1-0.2)(\dfrac{1.96}{0.04})^2=384.16\approx385](https://tex.z-dn.net/?f=n%3D0.2%281-0.2%29%28%5Cdfrac%7B1.96%7D%7B0.04%7D%29%5E2%3D384.16%5Capprox385)
Required sample size = 385
If p is unknown, then required sample size = ![n=0.25(\dfrac{z^*}{E})^2](https://tex.z-dn.net/?f=n%3D0.25%28%5Cdfrac%7Bz%5E%2A%7D%7BE%7D%29%5E2)
, where E = Margin of error , z* =critical z-value.
z-value for 95% confidence = 1.96
E = 0.04 (given)
So, ![n=0.25(\dfrac{1.96}{0.04})^2=600.25\approx601](https://tex.z-dn.net/?f=n%3D0.25%28%5Cdfrac%7B1.96%7D%7B0.04%7D%29%5E2%3D600.25%5Capprox601)
Required sample size = 601.