In a poll to estimate presidential popularity each person in

In a poll to estimate presidential popularity, each person in a random sample of 990 voters was asked to agree with one of the following statements:

A total of 700 respondents selected the first statement, indicating they thought the president was doing a good job.

Construct a 90% 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 =    0.707070707          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.014464227          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.023791536          
lower bound = p^ - z(alpha/2) * sp =   0.683279171          
upper bound = p^ + z(alpha/2) * sp =    0.730862243          
              
Thus, the confidence interval is              
              
(   0.683279171   ,   0.730862243   ) [ANSWER]

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b)

YES, because the whole interval is above 0.50. [ANSWER]