Question

The faculty members at McAdenville High School want to determine whether there are enough students to have a Winter Formal. Sixty-three of the 150 students surveyed said they would attend the Winter Formal. Construct and interpret a 99% confidence interval for p.

Answer 1

We are 99% confident that about (31.6 to 52.38) % of population would attend the Winter Formal.

Explanation:

Given:

- The sample proportion p = 63 out of 150

- The sample size n = 150

Find:

- The required confidence interval and its interpretation.

Solution:

- To develop CI at 99%, we need Z-score value at significance level a = 1 - CI.

a = 1 - 0.99 = 0.01

CI: Z_a/2 = Z_0.005 = 2.58

-The formula for developing the confidence interval for any proportion p is given by:

`CI = p +/- Z_a/2 * \sqrt{(p*(1-p))/(n) }`

- We can now determine the 99% confidence interval for p using above expression.

p = 63 / 150 = 0.42

1-p = 0.58

`CI = 0.42 +/- 2.58 * \sqrt{(0.42*(0.58))/(150) }\\\\CI = 0.42 +/- 0.10397\\\\0.316 < p < 0.5238`

- We are 99% confident that about (31.6 to 52.38) % of population would attend the Winter Formal.