2238 Final Election Poll Gallups final presidential election

22.38 Final Election Poll. Gallup\'s final presidential election poll was conducted November 1-4 2012. The poll included a random sample of 2551 adults, aged 18 and over, living in all 50 U.S. States and the District of Columbia, who were identified as likely to vote. Forty-eight percent of these likely voters said they would vote for Barack Obama. Does this provide evidence that, among al likely voters at the time the poll was conducted, less than half supported Barack Obama? (4 step problem)

Solution

As significance level is not given, we assume it is 0.05.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.5
Ha:   p   <   0.5
As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.48      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.009899535      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.020297008      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.021676294      
significance level =    0.05      

As P < 0.05, we REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that less than half supported Barack Obama. [CONCLUSION]