Question

A poll asked whether states should be allowed to conduct random drug tests on elected officials. Of 14 comma 472 ​respondents, 87​% said​ "yes." a. Determine the margin of error for a​ 99% confidence interval. b. Without doing any​ calculations, indicate whether the margin of error is larger or smaller for a​ 90% confidence interval. Explain your answer.

Answer 1

a)

Level of Significance,   α =    0.01          
Number of Items of Interest,   x =   12590.64          
Sample Size,   n =    14472          
                  
Sample Proportion ,    p̂ = x/n =    0.870          
z -value =   Zα/2 =    2.576   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0028          
margin of error , E = Z*SE =    2.576   *   0.0028   =   0.0072

b)

the margin of error is smaller for a​ 90% confidence interval.

Because the z -value would be less for 90% confidence.

Thanks in advance!

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