Answer: a) 1267
b) 1509
Step-by-step explanation:
As per given , we have
Significance level : [tex]\alpha: 1-0.98=0.02[/tex]
Using the z-value table , the critical z value for 98% confidence : [tex]z_{\alpha/2}=2.33[/tex]
Margin of error : E= 0.03
Formula for sample size :
[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex] , where p is the prior estimate of population proportion.
a) p=0.70
Sample size : [tex]n=(0.7)(1-0.7)(\dfrac{2.33}{0.03})^2[/tex]
Simplify , we get
[tex]n=11266.74333333\approx1267[/tex]
Hence, the minimum sample size required = 1267
a) if no estimate of prior population proportion is given , we take p= 0.5
Sample size : [tex]n=(0.5)(1-0.5)(\dfrac{2.33}{0.03})^2[/tex]
Simplify , we get
[tex]n=1508.02777778\approx1509[/tex]
Hence, the minimum sample size required = 1509
