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tankabanditka [31]
2 years ago
9

The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and unive

rsities. Suppose we take a poll (random sample) of 3653 students classified as Juniors and find that 3005 of them believe that they will find a job immediately after graduation. What is the 99 % confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation. (0.812, 0.833) (0.806, 0.839) (0.81, 0.835) (0.816, 0.829)
Mathematics
1 answer:
Murrr4er [49]2 years ago
5 0

Answer:

(0.806, 0.839)

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}.

Suppose we take a poll (random sample) of 3653 students classified as Juniors and find that 3005 of them believe that they will find a job immediately after graduation.

This means that n = 3653, \pi = \frac{3005}{3653} = 0.823

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}} = 0.823 - 2.575\sqrt{\frac{0.823*0.177}{3653}} = 0.806

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.823 + 2.575\sqrt{\frac{0.823*0.177}{3653}} = 0.839

The answer is (0.806, 0.839)

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