Answer: 359
Step-by-step explanation:
When prior estimate of population proportion is given , then the formula we use to find the sample size is given by :-
[tex]n=p(1-p)(\dfrac{z^*}{E})^2[/tex]
, 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 :
[tex]n=(0.37)(1-0.37)(\dfrac{(1.96)}{0.05})^2[/tex]
[tex]\Rightarrow\ n=(0.37)(0.63)(39.2)^2[/tex]
[tex]\Rightarrow\ n=0.2331\times1536.64\\\\\Rightarrow\ n=358.190784\approx359[/tex] [Rounded to next integer.]
Hence, the required minimum sample size = 359
