Question

Question 5 options: A high school principal wishes to estimate how well his students are doing in math. Using 40 randomly chosen tests, he finds that 77% of them received a passing grade. Create a 99% confidence interval for the population proportion of passing test scores.

Answer 1

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 = $\widehat{(p)}$ = $77\%$ = .77

1 - $\widehat{(p)}$ = 1 - .77 =.23

$\alpha$ = 1 - confidence interval = 1 - .99 = .01

$z_{\frac{\alpha}{2}}$ = $z_{\frac{.01}{2}}$ = 2.58

99% confidence interval for the population proportion of passing test scores=

$\widehat{(p)}\pm z_{\frac{\alpha}{2}} \sqrt{\frac{\widehat{(p)} (1 - \widehat{p})}{n}}$

= $.77\pm z_{\frac{.01}{2}} \sqrt{\frac{{(.77)} (.23)}{40}}$

= $.77\pm 0.1713$

= $(.77 + 0.1713 , .77 - 0.1713)$

= ( 0.5987 , 0.9413 )