# A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed to be 95% confident that the sample proportion will not differ from the true proportion by more than 6%?

1 answer

###### Question:

A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed to be 95% confident that the sample proportion will not differ from the true proportion by more than 6%?

## Answers

Answer: 267Step-by-step explanation:if we the prior proportion of population doesn't exist , then the formula to find the sample size is given by :-[tex]n=0.25\times(\dfrac{z_{\alpha/2}}{E})^2[/tex]Given : Confidence level : 0.95Significance level : [tex]\alpha: 1-0.95=0.05[/tex]Critical value : [tex]z_{\alpha/2}=1.96[/tex]Margin of error : [tex]E=0.06[/tex]Then , the required sample size will be :-[tex]n=0.25\times(\dfrac{1.96}{0.06})^2\\\\\Rightarrow\ n=266.777777778\approx267[/tex]Hence, the minimum required sample size = 267

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