Chapter 12 Inference for Proportions

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# Chapter 12 Inference for Proportions - PowerPoint PPT Presentation

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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### Chapter 12Inference for Proportions

AP Statistics

12.1 – Inference for a Population Proportion

• 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)
• 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
• 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
• 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
• 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)
• 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!