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almond37 [142]
2 years ago
7

Out of 100 people sampled, 42 had kids. Based on this, construct a 99% confidence interval for the true population proportion of

people with kids. Give your answers as decimals, to three places.
Mathematics
1 answer:
maksim [4K]2 years ago
7 0

Answer:

The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).

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 z-score that has a p-value of 1 - \frac{\alpha}{2}.

Out of 100 people sampled, 42 had kids.

This means that n = 100, \pi = \frac{42}{100} = 0.42

99% confidence level

So \alpha = 0.01, z is the value of Z that has a p-value 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}} = 0.42 - 2.575\sqrt{\frac{0.42*0.58}{100}} = 0.293

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 + 2.575\sqrt{\frac{0.42*0.58}{100}} = 0.547

The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).

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