The movie 2012 is based on several doomsday prophecies as di

The movie “2012” is based on several doomsday prophecies as disparate as the Mayan calendar, numerological constructions, and messages from extraterrestrial beings. As a rational thinking statistician, you decide to find out what proportion of the U.S. population actually believes in these prophecies. You take a randomly collected sample of 350 people and discover that 45 of them believe at least “somewhat” in the predictions. Construct a 95% confidence interval for the proportion of U.S. population who believe at least “somewhat” in doomsday prophecies. (Show your work or formula.). Interpret the interval

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n = 45/350 =    0.128571429          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.017891803          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.03506729          
lower bound = p^ - z(alpha/2) * sp =   0.093504139          
upper bound = p^ + z(alpha/2) * sp =    0.163638718          
              
Thus, the confidence interval is              
              
(   0.093504139   ,   0.163638718   ) [ANSWER]