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Ne4ueva [31]
2 years ago
12

In a​ poll, 37​% of the people polled answered yes to the question​ "Are you in favor of the death penalty for a person convicte

d of​ murder?" The margin of error in the poll was 5​%, and the estimate was made with 94​% confidence. At least how many people were​ surveyed?
Mathematics
2 answers:
Kay [80]2 years ago
5 0

Answer:

The number of people ​surveyed was 330.

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for the population proportion is:

CI=\hat p\pm z_{\alpha/2}\cdot \sqrt{\frac{\hat p(1-\hat p)}{n}}

The margin of error for this interval is:

MOE= z_{\alpha/2}\cdot \sqrt{\frac{\hat p(1-\hat p)}{n}}

The information provided is:

\hat p=0.37\\MOE=0.05\\\text{Confidence level}=0.94\\\Rightarrow \alpha=0.06

The critical value of <em>z</em> for 94​% confidence level is, <em>z</em> = 1.88.

*Use a <em>z</em>-table.

Compute the value of <em>n</em> as follows:

MOE= z_{\alpha/2}\cdot \sqrt{\frac{\hat p(1-\hat p)}{n}}

      n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}

         =[\frac{1.88\times \sqrt{0.37(1-0.37)}}{0.05}]^{2}\\\\=(18.153442)^{2}\\\\=329.5475\\\\\approx 330

Thus, the number of people ​surveyed was 330.

Firdavs [7]2 years ago
4 0

Answer:

329  people were​ surveyed

Step-by-step explanation:

Percent of people polling yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?"= 37 %

Margin error in the poll=5%

Confidence Interval=94%

The alpha value =1-0.94= 0.06

The Z ( critical value) for Confidence Interval of 94% =1.88

The sample size is given by

n=pq(\frac{z}{e})^2

where, p=0.37, q=0.63,  e= 5/100= 0.05, z=1.88

therefore,

n=0.37\times0.63(\frac{1.88}{0.05})^2

=329.54745

=329  people were​ surveyed

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