Confidence Interval for a Single Proportion p-hat, not phat

Conditions for a Confidence Interval In order for a confidence interval for a proportion to be valid, we must make sure a few conditions are met. First, we must make sure that our sample is a simple random sample from our population. This makes sure that our sample is representative. We must also look at the successes and failures in our sample. This varies from person to person, but I have been taught that n*p-hat and n*(1-p-hat) must be greater than or equal to 5. The video below says that these must be greater than 10, but I am sticking with 5.

Form of Interval The basic form of a confidence interval is point estimate plus or minus a critical value times standard error. For proportions, it looks like this: p-hat +or- Z*(sqrt(p-hat(1-p-hat)/n)), where p-hat is the sample proportion, and Z is the multiplier from the Z distribution.

Z multiplier The Z multiplier comes from the standard normal distribution, and is a Z score. There are four common confidence levels (90%, 95%, 98%, and 99%). Confidence Level Multiplier

Standard Error The formula for standard error for a single proportion is the square root of p-hat times 1-p- hat all divided by n, the sample size. This is a measurement of the standard deviation of the sampling distribution of the sample proportion. (I know it sounds complicated, but just think of it as standard deviation, adjusted for the fact that we have a sample of size n).

Margin of Error The margin of error for a confidence interval is simply the product of the Z multiplier and the standard error. This product is added and subtracted from the sample proportion to give us our confidence interval. See the video below on how to construct a confidence interval.