Mathematics
18.09.2022 08:13
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I need help quick!Please help me!

I need help quick!Please help me!
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hamaama
hamaama
4,9(13 marks)

Oh shucks, that's crazy man

amazinga
amazinga
4,8(1 marks)

The 99% confidence interval for the true proportion of Americans who were satisfied with the gun control laws in 2017 is (0.274, 0.526).

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}.

For this problem, we have that:

n = 100, \pi = 0.4

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}} = 0.4 - 2.575\sqrt{\frac{0.4*0.6}{100}} = 0.274

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 2.575\sqrt{\frac{0.4*0.6}{100}} = 0.526

The 99% confidence interval for the true proportion of Americans who were satisfied with the gun control laws in 2017 is (0.274, 0.526).

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