Given : Significance level : [tex]\alpha: 1-0.99=0.01[/tex]
Critical value : [tex]z_{\alpha/2}=2.576[/tex]
Margin of error : [tex]E=5[/tex]
Standard deviation : [tex]\sigma=6[/tex]
The formula to find the sample size :-
[tex]n=(\dfrac{z_{\alpha/2}\times\sigma}{E})^2[/tex]
Then, the sample size will be :-
[tex]n=(\dfrac{(2.576)\times6}{5})^2\\\\=(3.0912)^2=9.55551744\approx10[/tex]
The minimum final size sample required is 10.
If only 30 percent of households have a cat, then the proportion of households have a cat = 0.3
The formula to find the sample size :-
[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex]
Then, the sample size will be :-
[tex]n=0.3(1-0.3)(\dfrac{(2.576)}{5})^2\\\\=(0.21)(0.5152)^2=0.0557405184\approx1[/tex]
Hence, the initial number of households that need to be contacted =1
