isabellainksow87vn

07.12.2021 •

Mathematics

Which of the following is a solution to the inequality below?

–2w > –4

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Ответ:

kingyogii

21.10.2020

Mathematics

A sample of 595 should be obtained.

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

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

Estimate of 0.55

This means that $\pi = 0.55$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so Z = 1.96 .

What sample size should be obtained if she wishes the estimate to be within a margin of error of 0.04?

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.55*0.45}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.55*0.45}$

$\sqrt{n} = \frac{1.96\sqrt{0.55*0.45}}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.55*0.45}}{0.04})^2$

n = 594.2

Rounding up,

A sample of 595 should be obtained.

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Which of the following is a solution to the inequality below? –2w > –4