Answer: 833
Step-by-step explanation:
When the prior population proportion (p) is known , then the formula to find the minimum sample size is given by :-
![n=p(1-p)(\dfrac{z_{c}}{E})^2](https://tex.z-dn.net/?f=n%3Dp%281-p%29%28%5Cdfrac%7Bz_%7Bc%7D%7D%7BE%7D%29%5E2)
where,
is the z-score for confidence level (c) and E = the margin of error .
Given : A prior study estimated as 34%.
i.e. p= 0.34
Confidence level = 0.90
Critical z-score for 90% confidence level : ![z_{c}1.645](https://tex.z-dn.net/?f=z_%7Bc%7D1.645)
Margin of error : E= 0.027
then , the sample size = ![n=0.34(1-0.34)(\dfrac{1.645}{0.027})^2](https://tex.z-dn.net/?f=n%3D0.34%281-0.34%29%28%5Cdfrac%7B1.645%7D%7B0.027%7D%29%5E2)
Simplify ,
![n=832.9657\approx833](https://tex.z-dn.net/?f=n%3D832.9657%5Capprox833)
Hence, the minimum sample size=833