# Proportion Difference Standard Error

test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers confidence interval for difference in proportions calculator Probability Bayes rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific Financial standard error of difference between two proportions calculator Calculator books AP calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews

## Standard Error Two Proportions Calculator

Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Confidence Interval: Difference Between Proportions This lesson describes how to construct a confidence interval for## 2 Proportion Z Interval Conditions

the difference between two sample proportions, p1 - p2. Estimation Requirements The approach described in this lesson is valid whenever the following conditions are met: Both samples are simple random samples. The samples are independent. Each sample includes at least 10 successes and 10 failures. The Variability of the Difference Between Proportions To construct a confidence the confidence interval for the difference between two independent proportions interval for the difference between two sample proportions, we need to know about the sampling distribution of the difference. Specifically, we need to know how to compute the standard deviation or standard error of the sampling distribution. The standard deviation of the sampling distribution is the "average" deviation between all possible sample differences (p1 - p2) and the true population difference, (P1 - P2). The standard deviation of the difference between sample proportions σp1 - p2 is: σp1 - p2 = sqrt{ [P1 * (1 - P1) / n1] * [(N1 - n1) / (N1 - 1)] + [P2 * (1 - P2) / n2] * [(N2 - n2) / (N2 - 1)] } where P1 is the population proportion for sample 1, P2 is the population proportion for sample 2, n1 is the sample size from population 1, n2 is the sample size from population 2, N1 is the number of observations in population 1, and N2 is the number of observations in population 2. Whetest AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability

## 2 Proportion Z Interval Example

Bayes rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator confidence interval for two population proportions calculator books AP calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary confidence interval difference in proportions ti-84 AP practice exam Problems and solutions Formulas Notation Share with Friends Hypothesis Test: Difference Between Proportions This lesson explains how to conduct a hypothesis test to determine whether http://stattrek.com/estimation/difference-in-proportions.aspx?Tutorial=AP the difference between two proportions is significant. The test procedure, called the two-proportion z-test, is appropriate when the following conditions are met: The sampling method for each population is simple random sampling. The samples are independent. Each sample includes at least 10 successes and 10 failures. Each population is at least 20 times as big as its http://stattrek.com/hypothesis-test/difference-in-proportions.aspx?Tutorial=AP sample. This approach consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. State the Hypotheses Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The table below shows three sets of hypotheses. Each makes a statement about the difference d between two population proportions, P1 and P2. (In the table, the symbol ≠ means " not equal to ".) Set Null hypothesis Alternative hypothesis Number of tails 1 P1 - P2 = 0 P1 - P2 ≠ 0 2 2 P1 - P2 > 0 P1 - P2 < 0 1 3 P1 - P2 < 0 P1 - P2 > 0 1 The first set of hypotheses (Set 1) is an example of a two-tailed test, since an extreme value on either side of the sampling distribution would cause a researcher to reject the null hypothesis. The other two sets of hypotheses (Sets 2 and 3) are one-tailed tests, since= 73/85 - 43/82 = 0.8588 - 0.5244 = 0.3344. The fourth step confidence interval is to compute p, the probability (or probability value). It is the probability of obtaining a difference between the proportions as large or larger than the confidence interval for difference observed in the experiment. Applying the general formula to the problem of differences between proportions where p1- p2 is the difference between sample proportions and is the estimated standard error of the difference between proportions. The formula for the estimated standard error is: where p is a weighted average of the p1 and p2, n1 is the number of subjects sampled from the first population, and n2 is the number of subjects sampled from the second population.