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jekas [21]
2 years ago
10

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
Mathematics
1 answer:
cupoosta [38]2 years ago
6 0

Answer:

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

Step-by-step explanation:

The confidence interval for population proportion is:

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

<u>Given:</u>

<em>n</em> = 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{\frac{\hat p(1-\hat p)}{n}}\\=0.102\pm 2.58\times\sqrt{\frac{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.

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