Answer: [tex](0.771,\ 0.829)[/tex]
Step-by-step explanation:
Given : Significance level : [tex]\alpha: 1-0.99=0.01[/tex]
Critical value : [tex]z_{\alpha/2}=2.576[/tex]
Sample size : n=1305
The proportion of tenth graders read above the eighth grade level. =[tex]p=\dfrac{1044}{1305}=0.8[/tex]
The confidence interval for population proportion is given by :-
[tex]p\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}\\\\=0.8\pm(2.576)\sqrt{\dfrac{0.8(1-0.8)}{1305}}\\\\\approx0.8\pm0.029\\\\=(0.771,\ 0.829)[/tex]
Hence, the 99% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.771,0.829) .
