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Ch 12 – Inference for Proportions YMS 12.1

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

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Ch 12 – Inference for Proportions YMS 12.1

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  1. Ch 12 – Inference for ProportionsYMS 12.1 Inference for a Population Proportion

  2. 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

  3. 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

  4. 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

  5. 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)

  6. Which to use in formulasand 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

  7. YMS 12.2 Comparing Two Proportions

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

  9. 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

  10. 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

  11. 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

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