how to calculate standard error of proportion

This formula is similar to the error bound formula for a mean, except that the “appropriate standard deviation” is different. P′ = the estimated proportion of successes ( p′ is a point estimate for p, the true proportion.) The confidence interval has the form ( p′ – EBP, p′ + EBP). P′ follows a normal distribution for proportions: (Recall that a proportion as the number of successes divided by n.) If we divide the random variable, the mean, and the standard deviation by n, we get a normal distribution of proportions with P′, called the estimated proportion, as the random variable. When n is large and p is not close to zero or one, we can use the normal distribution to approximate the binomial. (Sometimes the random variable is denoted as, read “P hat”.) The random variable P′ (read “P prime”) is that proportion,

To form a proportion, take X, the random variable for the number of successes and divide it by n, the number of trials (or the sample size). (There is no mention of a mean or average.) If X is a binomial random variable, then X ~ B( n, p) where n is the number of trials and p is the probability of a success. How do you know you are dealing with a proportion problem? First, the underlying distribution is a binomial distribution. The procedure to find the confidence interval, the sample size, the error bound, and the confidence level for a proportion is similar to that for the population mean, but the formulas are different. Confidence intervals can be calculated for the true proportion of stocks that go up or down each week and for the true proportion of households in the United States that own personal computers. Businesses that sell personal computers are interested in the proportion of households in the United States that own personal computers. Investors in the stock market are interested in the true proportion of stocks that go up and down each week. Often, election polls are calculated with 95% confidence, so, the pollsters would be 95% confident that the true proportion of voters who favored the candidate would be between 0.37 and 0.43: (0.40 – 0.03,0.40 + 0.03). For example, a poll for a particular candidate running for president might show that the candidate has 40% of the vote within three percentage points (if the sample is large enough).

During an election year, we see articles in the newspaper that state confidence intervals in terms of proportions or percentages.

How to calculate standard error of proportion