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AP STATISTICS LESSON 12 - 2

AP STATISTICS LESSON 12 - 2. COMPARING TWO PROPORTIONS. Confidence intervals for Comparing Two Proportions.

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AP STATISTICS LESSON 12 - 2

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  1. AP STATISTICSLESSON 12 - 2 COMPARING TWO PROPORTIONS

  2. 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 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

  3. 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. ^ ^ ^ ^

  4. Example 12.11 Page 704How Much Does Preschool Help? ^ ^ 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.

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