Answer: [tex]=(0.2232,0.2768)[/tex]
Step-by-step explanation:
The confidence interval for population proportion is given by :-
[tex]p\ \pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}[/tex]
Given : Sample size : [tex]n=1000[/tex]
The proportion of people selected consumers who had opportunities to send in a rebate claim form after purchasing a product said they never did so =[tex]\dfrac{250}{1000}=0.25[/tex]
Significance level : [tex]1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
Now, the 95% confidence Interval for the true proportion of such consumers who never apply for a rebate will be :-
[tex]0.25\ \pm (1.96)\sqrt{\dfrac{0.25(1-0.25)}{1000}}\\\\\approx0.25\pm0.0268\\\\=(0.2232,\ 0.2768)[/tex]
Hence, a confidence Interval for the true proportion of such consumers who never apply for a rebate .
