Question

A sample of 1000 college students at NC State University were randomly selected for a survey. Among the survey participants, 102 students suggested that classes begin at 8 AM instead of 8:30 AM. The sample proportion is 0.102. What is the upper endpoint for the 99% confidence interval

Answer 1

The upper endpoint of the 99% confidence interval for population proportion is 0.13.

Explanation:

The confidence interval for population proportion is:

`CI=\hat p\pm z_(\alpha /2)\sqrt{(\hat p(1-\hat p))/(n)}`

Given:

n = 1000

`\hat p` = 0.102

`z_(\alpha /2)=z_(0.01/2)=z_(0.005)=2.58`

*Use the standard normal table for the critical value.

Compute the 99% confidence interval for population proportion as follows:

`CI=\hat p\pm z_(\alpha /2)\sqrt{(\hat p(1-\hat p))/(n)}\\=0.102\pm 2.58*\sqrt{(0.102(1-0.102))/(1000)}\\=0.102\pm0.0248\\=(0.0772, 0.1268)\\\approx (0.08, 0.13)`

Thus, the upper limit of the 99% confidence interval for population proportion is 0.13.