Ch 12 – Inference for Proportions YMS 12.1 Inference for a Population Proportion

Ch 9 Sampling Distributions is an unbiased estimator of population proportion p Standard deviation of is if the population is at least 10 times n Sampling distribution of is approximately normal if np and n(1-p) are at least 10 Use z-scores to standardize

Conditions for Inference To be representative: Data are from an SRS from the population of interest To accurately calculate standard deviation: Population is at least 10 times n To use normal calculations: Counts of successes/failures must be at least 10

Test of Significance Ho: p = po Standard Error Replacing p with in standard deviation formula Test of Significance Ho: p = po Verify that npo and n(1-po) are at least 10 Formula Confidence Interval Verify that n and n(1- ) are at least 10 Form

Choosing the Sample Size Margin of error Use a guess for p* Based on previous data Use the conservative estimate of 0.5 (unless you believe is closer to 0 or 1 because then p* = 0.5 will give you a much larger sample size than necessary)

Which to use in formulas and conditions? Hypothesis Tests Use po because that is the distribution you’re comparing your result to Confidence Intervals Use because you don’t have any other values (remember you’re using the CI to estimate the true proportion p) p698 #12.14-12.15, 12.17

Comparing Two Proportions YMS 12.2 Comparing Two Proportions

Sampling Distribution of When samples are large, the sampling distribution is approximately normal. Mean Variance

Confidence Intervals for Comparing Two Proportions Same form as for two means and standard error is replacing p with Conditions are still SRS, a population at least 10 times n, but now n1 , n1(1- ), n2 , and n2(1- ) are all greater than 5 p706 #12.22-12.23

Pooled Sample Proportion Because both samples actually come from one huge population, we combine the sample results to estimate the unknown population proportion p Formula

Significance Tests for Two Props Replace and with pooled in standard error formula and the conditions for count of successes and failures Other conditions remain the same! Test Stat p707 #12.24-12.26 A Civil Action – text, video and article