Answer: 2172
Step-by-step explanation:
Formula to find the sample size n , if the prior estimate of the population proportion(p) is known:
[tex]n= p(1-p)(\dfrac{z^*}{E})^2[/tex] , where E= margin of error and z* = Critical z-value.
Let p be the population proportion of adults have consulted fortune tellers.
As per given , we have
p= 0.20
E= 0.02
From z-table , the z-value corresponding to 98% confidence interval = z*=2.33
Then, the required sample size will be :
[tex]n= 0.20(1-0.20)(\dfrac{2.33}{0.02})^2[/tex]
[tex]n= 0.20(0.80)(116.5)^2[/tex]
[tex]n= 2171.56\approx2172[/tex]
Hence, the required sample size = 2172
