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Chapter 18 Inference about a Population Proportion

Chapter 18 Inference about a Population Proportion. 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. “ p-hat”.

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Chapter 18 Inference about a Population Proportion

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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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