Students are reluctant to report cheating by other students

Students are reluctant to report cheating by other students. A student project put this question to an SR Sof 172 undergraduates at a large unviersity: \"You witness two students cheating on a quiz. Do you go to the professor?\" Only 19 answered \"yes\". Give a 95% confidence interval for the proportion of all undergraduates at this university who would report cheating.

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.110465116          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.023901758          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.046846585          
lower bound = p^ - z(alpha/2) * sp =   0.063618531          
upper bound = p^ + z(alpha/2) * sp =    0.157311701          
              
Thus, the confidence interval is              
              
(   0.063618531   ,   0.157311701   )   [ANSWER]