Chapter 12Inference for Proportions
AP Statistics
12.1 – Inference for a Population Proportion
p̂
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.
p̂
p̂
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
p̂
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))
How about a 95% confidence interval?
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!
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