Question

A poll finds that 57% of the population approves of the job that the President is doing; the poll has a margin of error of 2% (assuming a 95% degree of confidence).
What is the 95% confidence interval for the true population percentage that approves of the President's performance?

Answer 1

Answer on Question #48832 – Math – Statistics and Probability

A poll finds that 57% of the population approves of the job that the President is doing; the poll has a margin of error of 2% (assuming a 95% degree of confidence).

What is the 95% confidence interval for the true population percentage that approves of the President’s performance?

Solution

The 95% confidence interval for the true population percentage that approves of the President’s performance is

$$(\bar{p} - ME; \bar{p} + ME),$$

where $\bar{p} = 57\%$ and $ME = 2\%$. So,

$$(57\% - 2\%; 57\% + 2\%) = (55\%; 59\%).$$

Answer: (55%; 59%).

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