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Inference about Population Proportion: Methods & Examples

Learn the principles of estimating population proportion with sample proportions, confidence intervals, and significance tests. Explore conditions for inference, choosing sample size, and practical examples. Enhance your statistical knowledge today!

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Inference about Population Proportion: Methods & Examples

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  1. Chapter 18Inference about a Population Proportion

  2. Outline • The sample proportion • The sampling distribution of • Conditions for inference • Large-sample confidence intervals for a population proportion • Choosing the sample size • Significance tests for a proportion

  3. “p-hat” 1. The Sample proportion • The proportion of a population that has some outcome (“success”) is p. • The proportion of successes in a sample is measured by the sample proportion:

  4. 2. The sampling distribution of

  5. 3. Conditions for inference

  6. Standard Error of Since the population proportion p is unknown, the standard deviation of the sample proportion will need to be estimated by substituting for p.

  7. 4. Large-sample confidence intervals for a population proportion

  8. Examples • Example 18.4 Estimating risky behavior (Page 476) • Example 18.5 Are the conditions met? (Page 476) • Exercise 18.8 No confidence interval. (Page 477)

  9. 5. Accurate C.I. for a proportion • Example 18.6 (P479) Shaq’s free shows

  10. 6. Choosing the sample size • The margin of error in our confidence interval is • We may like to choose the sample size n to achieve a certain margin of error.

  11. The sample size

  12. Guess the sample proportion: • Since we don’t know prior to sampling, we will have to use a guess p* for . There are two ways to do this: • Use a guess p* based on a pilot study or on past experience. • Use p*=0.50 as the guess. This guess is conservative, as it gives a margin of error bigger than the true margin of error. (Conservative)

  13. Example • Example 18.7 Planning a poll (Page 482)

  14. 7. Significance tests for a proportion

  15. Examples • Example 18.8 Is this coin fair? (Page 484) • Example 18.9 Estimating the chance of head (Page 485)

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