In a poll to estimate presidential popularity each person in

In a poll to estimate presidential popularity, each person in a random sample of 1,510 voters was asked to agree with one of the following statements:

A total of 625 respondents selected the first statement, indicating they thought the president was doing a good job.

Construct a 95% confidence interval for the proportion of respondents who feel the president is doing a good job. (Use Student\'s t Distribution Table.) (Round your answers to 3 decimal places.)

Based on your interval in part (a), is it reasonable to conclude that a majority of the population believes the president is doing a good job?

Solution

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.413907285          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.012674949          
              
Now, for the critical z,              

alpha =   0.05          

Thus, z(alpha) =    1.644853627          
Thus,              
      
      
upper bound = p^ + z(alpha/2) * sp =    0.434755721 [ANSWER]

*************************          
              
b)

NO, because the maximum proportion is less tha 0.5. [ANSWER, NO]