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

We are 99% confident interval for the population proportion of passing test scores between ( 0.5987 and 0.9413 )

Explanation:

Given -

n = 40

Population proportion =
`\widehat{(p)}` =
`77\%` = .77

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

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

`z_{(\alpha)/(2)}` =
`z_{(.01)/(2)}` = 2.58

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

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

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

=
`.77\pm 0.1713`

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

= ( 0.5987 , 0.9413 )