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ivolga24 [154]
3 years ago
11

Which of the following statements is true about the number 30/2

Mathematics
1 answer:
jeka943 years ago
7 0

Answer:

15

Step-by-step explanation:

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The sample size needed if the margin of error of the confidence interval is to be about 0.04 is 18.

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}}

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.

Past studies suggest this proportion will be about 0.15

This means that p = 0.15

Find the sample size needed if the margin of error of the confidence interval is to be about 0.04

This is n when M = 0.04. So

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

0.04 = 1.96\sqrt{\frac{0.15*0.85}{n}}

0.04\sqrt{n} = 1.96\sqrt{0.15*0.85}

\sqrt{n} = \frac{1.96\sqrt{0.15*0.85}}{0.04}

(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.15*0.85}}{0.04})^{2}

n = 17.5

Rounding up

The sample size needed if the margin of error of the confidence interval is to be about 0.04 is 18.

8 0
3 years ago
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