Question

In a poll to estimate presidential popularity, each person in a random sample of 1,310 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 625 respondents selected the first statement, indicating they thought the president was doing a good job.

1. Construct a 95% confidence interval for the proportion of respondents who feel the president is doing a good job. (Round your answers to 3 decimal places.)

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 625 / 1310 = 0.477

1 - = 1 - 0.477 = 0.523

Z_/2 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.477 * 0.523) /1310 )

= 0.027

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.477 - 0.027 < p < 0.477 + 0.027

0.450 < p < 0.504

The 95% confidence interval for the population proportion p is : 0.450 . 0.504