In a poll to estimate presidential popularity each person in

In a poll to estimate presidential popularity, each person in a random sample of 1,470 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)
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=625
Sample Size(n)=1470
Sample proportion = x/n =0.425
Confidence Interval = [ 0.425 ±Z a/2 ( Sqrt ( 0.425*0.575) /1470)]
= [ 0.425 - 1.96* Sqrt(0) , 0.425 + 1.96* Sqrt(0) ]
= [ 0.4,0.45]

b)
No. Because it is less than 50%