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:
The president is doing a good job.
The president is doing a poor job.
I have no opinion.
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. (Round your answers to 3 decimal places.)
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
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