Chapter 12: Inference for Proportions

BY: Lindsey Van Cleave

12.1: Inference For a Population Proportion

• The statistic that estimates the parameter p is the sample proportion:

12.1: Inference For a Population Proportion

• p is an unbiased estimator of the population proportion…

12.1: Inference For a Population Proportion

• The distribution of p can be assumed to be normal if…• 1. The population is at least 10 times the

sample.• 2. np is at least 10• 3. n(1-p) is at least 10

• Is p is found to be normal use the following formula to standardize it

12.1: Inference For a Population Proportion

• To test the null hypothesis H0: p=p0 that the unknown p has a specific value, p0, just replace p by p0 in the z statistic and in checking the values of np and n(1-p).

12.1: Inference For a Population Proportion

• In a confidence interval for p, we have no specific value to substitute. In large samples, p, will be close to p. So we replace p by p in determining the values of np and n(1-p). We also replace the standard deviation by the standard errror of p

12.1: Inference For a Population Proportion

• To determine the sample size n that will yield a level C confidence interval for a population proportion p with a specified margin of error m:

Comparing Two Proportions

• In a two-sample problem we want to compare two populations or the responses to two treatments based on two independent samples.

• We compare the population by doing inference about the difference p1-p2

Comparing Two Proportions

• Standard Deviation:

• Confidence Interval

Comparing Two Proportions

• Don’t worry you can do all of the significance tests in your calculator:

• 1. STAT and then TESTS• #6: 2-PropZTest• Enter info and push calculate• Then there is your correct

response!