Question

A CNN poll was conducted from May 7 to May 10.  Among a random sample of 1001 registered voters, 511 of them supported Joe Biden. 503 out of these 1001 registered voters are democrats, and 87% of these 503 democrats supported Biden. Will the margin of error among democrats be greater than, less than, or equal to, that from all parties?  Explain

Answer 1

Margin of errors among democrat:

Level of Significance,   α =    0.05          
Number of Items of Interest,   x =   437.61          
Sample Size,   n =    503          
                  
Sample Proportion ,    p̂ = x/n =    0.870          
z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0150          
margin of error , E = Z*SE =    1.960   *   0.0150   =   0.0294

Margin of errors for parties:

Level of Significance,   α =    0.05          
Number of Items of Interest,   x =   503          
Sample Size,   n =    1001          
                  
Sample Proportion ,    p̂ = x/n =    0.502          
z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      

                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0158          
margin of error , E = Z*SE =    1.960   *   0.0158   =   0.0310

Will the margin of error among democrats be less than that from all parties

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