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Andrews [41]
3 years ago
8

A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not. Determ

ine a 68 % confidence interval for the population proportion of college seniors who plan to attend graduate school. (Enter each answer rounded to three decimal places.)
Mathematics
1 answer:
Hunter-Best [27]3 years ago
4 0

Answer:

The 68% confidence interval for the population proportion of college seniors who plan to attend graduate school is (0.16, 0.24).

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}.

A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not.

This means that n = 100, \pi = \frac{20}{100} = 0.2

68% confidence level

So \alpha = 0.32, z is the value of Z that has a pvalue of 1 - \frac{0.32}{2} = 0.84, so Z = 0.995.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 - 0.995\sqrt{\frac{0.2*0.8}{100}} = 0.16

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 + 0.995\sqrt{\frac{0.2*0.8}{100}} = 0.24

The 68% confidence interval for the population proportion of college seniors who plan to attend graduate school is (0.16, 0.24).

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