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Chapter 12 Inference for Proportions

Chapter 12 Inference for Proportions. AP Statistics 12.1 – Inference for a Population Proportion. Conditions for Inference of Step II: (z – procedures). Ch 9: The sample proportion is an unbiased estimator of the true population proportion p. = p

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Chapter 12 Inference for Proportions

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  1. Chapter 12Inference for Proportions AP Statistics 12.1 – Inference for a Population Proportion

  2. Conditions for Inference of Step II: (z – procedures) • Ch 9: The sample proportion is an unbiased estimator of the true population proportion p. = p • Ch 9: Standard deviation of • The data are Randomly and Independently selected from the population of interest.

  3. Conditions for Inference of (z – procedures) • The population size is at least ten times the sample  allows us to use the formula for standard error.N≥10n • theThe sample is sufficiently large to insure Normality of the sampling distribution of • Confidence Intervals: Use • Tests of Significance: Use

  4. Cautions for Proportions • Often proportions use surveys . . . • Many different biases can be introduced: • Undercoverage bias • Non-response bias • Lack or Realism bias – lying, uncomfortable • More likely that sample proportions are overestimates or underestimates of the true population proportion.

  5. Z – procedures: Step III • Confidence Intervals: (statistic) ± (critical value) SE(statistic) • Tests of Significance: • where is the initial pop. Claim P-value = normalcdf(z(low), z(high))

  6. How about a 95% confidence interval?

  7. Choosing the Sample Size • Trying to find the value of n • Recall that • But we don’t know so we will guess • 1. Use a guess based on previous studies • 2. Use = 0.5 as the guess . . . Why? • Sample size for a desired margin of error:

  8. Chavez (take 2) • What if we only want a 2.5% ME? • What if we only want a 2% ME? • Note: Smaller ME’s require larger sample sizes!

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