COMPARING TWO PROPORTIONS AP STATISTICS LESSON 12 - 2 COMPARING TWO PROPORTIONS

Confidence intervals for Comparing Two Proportions Draw an SRS of size n from a population having proportion p of successes and draw an independent SRS of size n from another population having proportion p of successes. When n and n are large, an approximate level C confidence interval for p1 – p2 is (p1 – p2) ± z* SE In this formula the standard error (SE) of p1 – p2 is SE = √p 1(1 – p1)/n1 + p 2(1 – p2)/n2 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Confidence Interval (continued…) And z* is the upper (1 – C)/2 standard normal critical value. Conditions: In practice, use this confidence interval when the populations are at least 10 times as large as the samples and n 1p1, n 1(1 – p1), n2 p2 and n 2(1 – p2) are all 5 or more. ^ ^ ^ ^

Example 12.11 Page 704 How Much Does Preschool Help? Population Population Description Sample Size Sample Proportion 1 Control N1 = 61 P1 = 0.803 2 Preschool N2 = 62 P2 = 0.613 ^ ^ We are 95% confident that the percent needing social services is somewhere between 3.3% and 34.7% lower among people who attended preschool. The confidence interval is wide because the samples are quite small.