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!