Inference for a Population Proportion

1
Inference for a Population Proportion

• Previously our discussions of inference where
  about making inference on population means.
• This chapter teaches us how to make inference
  about a proportion of outcomes in a population.

2
Inference for a Population Proportion

• Example 12.1 12.3

3
Inference for a Population Proportion

• We are interested in the unknown proportion p of
  a population that has some outcome.
• The outcome we are looking for is called a
  success
• Consider example 12.1 170 of the 2673 people
  surveyed said they had had more than one sexual
  partner.
• The sample proportion in this problem is

4
Inference for a Population Proportion

• Remember from before that phat is an unbiased
  estimator of the sample proportion p and the
  standard deviation can be found as long as
• The population is at least 10 times as large as
  the sample
• And np and n(1-p) are at least 10.
• If all this takes place we can standardized the
  value and the z statistic is approximately a
  normal curve.

5
Inference for a Population Proportion

• The conditions for inference about a proportion,
  and using a 1Prop-Ztest are
• The data are an SRS from the population of
  interest.
• The population is 10 times bigger than the
  sample.
• np and n(1-p) must be 10 or bigger.

6
Inference for a Population Proportion

• Example 12.4 Are the conditions met?

7
Inference for a Population Proportion

• The z procedures
• There are some really icky formulas for CI and
  Tests of significance, lucky for use our
  calculators will crunch the numbers for us!
• We are going to use a 1PropZTest.

8
Inference for a Population Proportion

• Examples 12.5 12.8

9
Inference for a Population Proportion

• Choosing the sample size
• When designing a study we may want to choose the
  sample size based on what will allow us the
  inference within a certain margin of error.
• m

10
Inference for a Population Proportion

• m
• z is the standard normal critical value for
  level of confidence.
• p is a guess based on a previous study or you
  can use 0.5 as a large estimator.

11
Inference for a Population Proportion

• Example 12.9 Determining Sample Size.