Mathematics: Wisconsin Public Radio wants to duplicate a survey conducted in 2011 that found that 68% of adults living in Wisconsin felt that the country was going in the wrong direction. How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 3%? Be sure to show all your work and round appropriately

They are not the same thing....

Wisconsin Public Radio wants to duplicate a survey

Ответ:

tammydbrooks43

29.01.2022

Mathematics

655 people would need to be surveyed.

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

In this question, we have that:

$\pi = 0.68$

The margin of error is:

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

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so Z = 1.645 .

How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 3%?

We need to survey n adults.

n is found when M = 0.03. So

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

$0.03 = 1.645\sqrt{\frac{0.68*0.32}{n}}$

$0.03\sqrt{n} = 1.645\sqrt{0.68*0.32}$

$\sqrt{n} = \frac{1.645\sqrt{0.68*0.32}}{0.03}$

$(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.68*0.32}}{0.03})^{2}$

n = 654.3

Rounding up

655 people would need to be surveyed.

0,0(0 оценок)

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question