28 Misleading Survey Responses Voting records show that 61 o

28.

Misleading Survey Responses Voting records show that 61% of eligible voters actually did vote in a recent presidential election. In a survey of 1002 people, 70% said that they voted in that election (based on data from ICR Research Group). Use the survey results to test the claim that the percentage of all voters who say that they voted is equal to 61%. What do the results suggest?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.61
Ha:   p   =/=   0.61
As we see, the hypothesized po =   0.61      
As it is given,          
          
po =    0.61      
          
Getting the standard error of po, spo,          
          
spo = sqrt[po (1 - po) / n] =    0.015408606      
          
Getting the z statistic,          
p^ =    0.7      
z = (p^ - po)/spo =    5.840891638      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    5.19222E-09      
significance level =    0.05      
Comparing p and the significance value, we REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that the percentage of all voters who say that they voted is not equal to 61%.

This may suggest that some people do not want others to know that they did not vote, and say they actually voted.