In a random sample of 31 professional actors it was found th

In a random sample of 31 professional actors, it was found that 24 were extroverts. Find a 98% confidence interval for p.

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.774193548          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.075095186          
              
Now, for the critical z,              
alpha/2 =   0.01          
Thus, z(alpha/2) =    2.33          
Thus,              
Margin of error = z(alpha/2)*sp =    0.175          
lower bound = p^ - z(alpha/2) * sp =   0.589          
upper bound = p^ + z(alpha/2) * sp =    0.959          
              
Hence, it is OPTION B: 0.589 to 0.959. [ANSWER]