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 $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 152, \pi = \frac{96}{152} = 0.6316$

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:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6316 - 2.575\sqrt{\frac{0.6316*0.3684}{152}} = 0.5309$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6316 + 2.575\sqrt{\frac{0.6316*0.3684}{152}} = 0.7323$

The 99% confidence interval for the proportion of athletes who graduate is (0.5309, 0.7323).

4 0

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Daniel worked for 2 1/3 hours and earned $18.20, how much would he make if he worked 5 1/4 hours?

sdas [7]

I hope this helps you

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A car travels 288 miles in 4 hours and 30 minutes. How many miles does it travel per hour?

Archy [21]

It travels 64 miles per hour

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