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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

Chapter 12Inference for Proportions

AP Statistics

12.1 – Inference for a Population Proportion

conditions for inference of step ii z procedures
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.
conditions for inference of z procedures
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
cautions for proportions
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.
z procedures step iii
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))

choosing the sample size
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:
chavez take 2
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!