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 $Z = 1.96$ .

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.03 for the estimation of a population proportion?

We need a sample of n.

n is found when M = 0.03.

We have no prior estimate of $\pi$ , so we use the worst case scenario, which is $\pi = 0.5$

Then

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

$0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.03\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.03}$

$(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.03})^{2}$

$n = 1067.11$

Rounding up

A sample of 1068 is needed.

8 0

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The coordinates of point A on a grid are (5, −3). Point A is reflected across the x-axis to obtain point B. The coordinates of p

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Answer: (5,3)

Step-by-step explanation:

the formula used for a reflection across the x-axis is (x,-y)

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Marleny is creating a game of chance for her family. She has 5 different colored marbles in a bag: blue, red, yellow, white, and

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Answer:

Step-by-step explanation:

Got it right on brainly

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Translate the sentence into an equation.

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Answer:

b + 2 = 6

Step-by-step explanation:

This may not be the right answer, but its what I think it is.

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A local little league has a total of 60 ​players, of whom ​20% are right​-.handed. How many right​-handed players are​ there?

A local little league has a total of 60 players, of whom 20% are right-.handed. How many right-handed players are there?