Respuesta :
Answer:
We are 99% confident interval for the population proportion of passing test scores between ( 0.5987 and 0.9413 )
Step-by-step explanation:
Given -
n = 40
Population proportion = [tex]\widehat{(p)}[/tex] = [tex]77\%[/tex] = .77
1 - [tex]\widehat{(p)}[/tex] = 1 - .77 =.23
[tex]\alpha[/tex] = 1 - confidence interval = 1 - .99 = .01
[tex]z_{\frac{\alpha}{2}}[/tex] = [tex]z_{\frac{.01}{2}}[/tex] = 2.58
99% confidence interval for the population proportion of passing test scores=
[tex]\widehat{(p)}\pm z_{\frac{\alpha}{2}} \sqrt{\frac{\widehat{(p)} (1 - \widehat{p})}{n}}[/tex]
= [tex].77\pm z_{\frac{.01}{2}} \sqrt{\frac{{(.77)} (.23)}{40}}[/tex]
= [tex].77\pm 0.1713[/tex]
= [tex](.77 + 0.1713 , .77 - 0.1713)[/tex]
= ( 0.5987 , 0.9413 )
