Population proportion confidence interval?

Question

Use the given degree of confidence and sample data to construct a confidence interval for this population proportion p. n = 153, x = 138, 95 percent

Answer 1

The answer is from .855 to .949
... or 90.2% + or - 4.7%

This is very easy to do with a TI-83 or other statistical graphing calculator (choose 1-proportion z-interval). It is also easy with a computer that has a statistical software package.

If you need to do it by hand, you first of all calculate the point estimate (usually called p-hat), which is 138 / 153 = .90196

Then you calculate the margin of error. The formula is ...
E = Zc * SQR(p-hat * q-hat / n)
where Zc is the z-score associated with your level of confidence (for 95%, that z-score is 1.96
p-hat is the number we calculated above
q-hat = 1 - p-hat ... Here it's .09804
1.96 * SQR (.09196 * .09804 / 153 ) = .04712

The interval is the center (p-hat) + or - the margin of error.
You can either write it with +/- or you can literally subtract and add to get the bottom and top of the interval.