Answer: (-0.086, 0.026)
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 : Significance level : [tex]\alpha: 1-0.90=0.10[/tex]
Critical value : [tex]z_{\alpha/2}=1.645[/tex]
Sample size : [tex]n_1=400,\ n_2=400[/tex]
[tex]p_1=0.61,\ p_2=0.64[/tex]
The 90% confidence interval for the difference in the population proportions will be :-
[tex]0.61-0.64\pm\ (1.645)\sqrt{\dfrac{0.61(1-0.61)}{400}+\dfrac{0.64(1-0.64)}{400}}\\\\\approx-0.03\pm0.056=(-0.03-0.056,-0.03+0.056)\\\\=(-0.086, 0.026)[/tex]
