18 Perception and Reality In a presidential election 308 out

18.

Perception and Reality In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won (based on data from ICR Survey Research Group). Use a 0.10 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.43
Ha:   p   =/=   0.43
As we see, the hypothesized po =   0.43      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.504091653      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.020028621      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    3.699288767      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.000216204      

significance level =    0.1      

Comparing p < 0.1, we   REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that the proportion of those who believe they voted the winning candidate is not the actual percentage, 43%.

This tells that the voters may either want to think they voted the candidate who one, or would tell others they voted for the winning candidate.