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Murljashka [212]
2 years ago
8

The National Assessment of Educational Progress (NAEP) includes a "long-term trend" study that tracks reading and mathematics sk

ills over time, and obtains demographic information. In the 2012 study, a random sample of 9000 17-year-old students was selected.24 The NAEP sample used a multistage design, but the overall effect is quite similar to an SRS of 17-year-olds who are still in school. In the sample, 51% of students had at least one parent who was a college graduate. Estimate, with 99% confidence, the proportion of all 17-year-old students in 2012 who had at least one parent graduate from college.
Mathematics
1 answer:
daser333 [38]2 years ago
7 0

Answer:

The 99% confidence interval estimate for the proportion of all 17-year-old students in 2012 who had at least one parent graduate from college is (0.4964, 0.5236).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

Sample of 9000, 51% of students had at least one parent who was a college graduate.

This means that n = 9000, \pi = 0.51

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.51 - 2.575\sqrt{\frac{0.51*0.49}{9000}} = 0.4964

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.51 + 2.575\sqrt{\frac{0.51*0.49}{9000}} = 0.5236

The 99% confidence interval estimate for the proportion of all 17-year-old students in 2012 who had at least one parent graduate from college is (0.4964, 0.5236).

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