Answer: [tex](-0.48,\ -0.04)[/tex]
Step-by-step explanation:
The confidence interval for the difference of two population proportion is given by :-
[tex](p_1-p_2)\pm z_{\alpha/2}\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}[/tex]
Given : The first sample consists of 20 people with 9 having a common attribute.
Here, [tex]n_1=20[/tex] , [tex]p_1=\dfrac{9}{20}=0.45[/tex]
[tex]n_2=2100 [/tex] , [tex]p_1=\dfrac{1492 }{2100}\approx0.71[/tex]
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
A 95% confidence interval for the difference of two population proportion will be :-
[tex](0.45-0.71)\pm z_{\alpha/2}\sqrt{\dfrac{0.45(1-0.45)}{20}+\dfrac{0.71(1-0.71)}{2100}}\\\\\approx -0.26\pm0.22\\\\=(-0.26-0.22,-0.26+0.22)\\\\=(-0.48,\ -0.04)[/tex]
