Answer:
The number of people surveyed was 330.
Step-by-step explanation:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\cdot \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
[tex]\hat p=0.37\\MOE=0.05\\\text{Confidence level}=0.94\\\Rightarrow \alpha=0.06[/tex]
The critical value of z for 94% confidence level is, z = 1.88.
*Use a z-table.
Compute the value of n as follows:
[tex]MOE= z_{\alpha/2}\cdot \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}[/tex]
[tex]=[\frac{1.88\times \sqrt{0.37(1-0.37)}}{0.05}]^{2}\\\\=(18.153442)^{2}\\\\=329.5475\\\\\approx 330[/tex]
Thus, the number of people surveyed was 330.
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
[tex]n=pq(\frac{z}{e})^2[/tex]
where, p=0.37, q=0.63, e= 5/100= 0.05, z=1.88
therefore,
[tex]n=0.37\times0.63(\frac{1.88}{0.05})^2[/tex]
=329.54745
=329 people were surveyed
