20 Twitter Poll The Pew Research Center conducted a survey o

20.

Twitter Poll The Pew Research Center conducted a survey of 1007 adults and found that 856 of them know what Twitter is. Use a 0.01 significance level to test the claim that more than 75% of adults know what Twitter is.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.75
Ha:   p   >   0.75
As we see, the hypothesized po =   0.75      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.850049652      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.013645388      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    7.332122015      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    1.13268E-13      
significance level =    0.01      

Comparing p < 0.01 , we   REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that more than 75% of adults know what Twitter is. [CONCLUSION]