In a poll to estimate presidential popularity, each person in a random sample of

Question

In a poll to estimate presidential popularity, each person in a random sample of 1,030 voters was asked to agree with one of the following statements:

1. The president is doing a good job.

2. The president is doing a poor job.

3. I have no opinion.

A total of 500 respondents selected the first statement, indicating they thought the president was doing a good job.

Construct a 98% 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?

Construct a 98% 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.)

Explanation / Answer

a.
Confidence Interval For Proportion
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)=500
Sample Size(n)=1030
Sample proportion = x/n =0.485
Confidence Interval = [ 0.485 ±Z a/2 ( Sqrt ( 0.485*0.515) /1030)]
= [ 0.485 - 2.326* Sqrt(0) , 0.485 + 2.33* Sqrt(0) ]
= [ 0.449,0.521]

b.
No, since th einterval lies below fifty percent in times

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