Question

If you want to be 95​% confident of estimating the population proportion to within a sampling error of plus or minus0.05 and there is historical evidence that the population proportion is approximately 0.37​, what sample size is​ needed? A sample size of nothing is needed. ​(Round up to the nearest​ integer.)

Answer 1

Answer: 359

Explanation:

When prior estimate of population proportion is given , then the formula we use to find the sample size is given by :-

`n=p(1-p)((z^*)/(E))^2`

, where p= prior estimate of population proportion

z*= critical-value.

E= Margin of sampling error.

As per given , we have

p=0.37

E= ± 0.05

We know that critical z-value corresponding to 95% confidence level = z*=1.960 [Using z-table]

Then, Required sample size :

`n=(0.37)(1-0.37)(((1.96))/(0.05))^2`

`\Rightarrow\ n=(0.37)(0.63)(39.2)^2`

`\Rightarrow\ n=0.2331*1536.64\\\\\Rightarrow\ n=358.190784\approx359` [Rounded to next integer.]

Hence, the required minimum sample size = 359