Question

In a​ poll, ​% of the people polled answered yes to the question​ are you in favor of the death penalty for a person convicted of​ murder? the margin of error in the poll was ​%, and the estimate was made with ​% confidence. At least how many people were​ surveyed?.

Answer 1

The number of people surveyed is 20

Finding Sample size:

In statistics, the sample size is the value of the number of individual samples used in an experiment. For example, if we are testing 100 samples of people who play cricket, then the sample size will be equal to 100.  

If a point of estimation is available then the formula for sample size n is given by      

Sample size n = p(1 - p)[ $Z_{\alpha /2}$/ E ]²    

Where p is the point of estimation

$Z_{\alpha /2}$ is the critical value

E is the margin of error        

Here we have

51​% of the people polled answered yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?"

Here estimated point p = 51% = 0.51

The margin of error E = 22​% = 0.22

The estimate was made with 95​% confidence.  

Then the critical value  $Z_{\alpha /2}$ = 1.96  

Here we need to find how many people were​ surveyed        

From the above observations,

n = p(1 - p)[ $Z_{\alpha /2}$/ E ]²            

=>  0.51 (1 - 0.51) [ 1.96 / 0.22 ]²            

=>  0.51 (0.49) [ 8.91 ]²

=>  0.51(0.49) (79.3718)

=>  19.83    

=> 20   (approximately )                          

Therefore, the number of people surveyed is 20

Learn more about Sample size problems at

https://brainly.com/question/17014563

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The Complete question:

In a​ poll, 51​% of the people polled answered yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?" The margin of error in the poll was 22​%, and the estimate was made with 95​% confidence. At least how many people were​ surveyed?

The minimum number of surveyed people was?