P′ = the estimated proportion of successes or sample proportion of successes ( p′ is a point estimate for p, the true population proportion, and thus q is the probability of a failure in any one trial.) (Sometimes the random variable is denoted as, read “P hat”.) The random variable P′ (read “P prime”) is the sample proportion, To form a sample 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 has a binary random variable and therefore is a binomial distribution. Because of this we will see the same basic format using the same three pieces of information: the sample value of the parameter in question, the standard deviation of the relevant sampling distribution, and the number of standard deviations we need to have the confidence in our estimate that we desire. While the formulas are different, they are based upon the same mathematical foundation given to us by the Central Limit Theorem. The procedure to find the confidence interval for a population proportion is similar to that for the population mean, but the formulas are a bit different although conceptually identical. 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. 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). When you calculate the standard deviation this way, you won’t need to trim the number, as it will automatically be trimmed to two decimals.Confidence Intervals 41 A Confidence Interval for A Population Proportionĭuring an election year, we see articles in the newspaper that state confidence intervals in terms of proportions or percentages. Going back to the Method 1 example where we were calculating the standard deviation for cells C2 to C11, you should write C2:C11. Next, in the Function Arguments window, enter the range for which you want to calculate the standard deviation into the text box next to Number1.Then, select Statistical, browse the list below and select either STDEV.P or STDEV.S.Now, click the arrow next to Or select a category to open the dropdown menu.After that, click the Insert Function button.Next, click the Formulas header in the Main Menu.Click on the cell where the deviation result will appear.
#Calculate standard error population proportion how to#
Let’s see how to get the deviations without typing the formulas. It is great when you’re in a crunch but don’t want to mess with the formulas. The next method is almost as fast as the first one and doesn’t require in-depth Excel knowledge.
In this example, you want to calculate STDEV.P for cells C2 to C11 and STDEV.S for cells C4 to C7. The values in the brackets denote the range of cells for which you want to calculate the standard deviation value. Click on the cell where you’d like the standard deviation value to be displayed.
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