Estimating a Population Proportion Textbook Section 8.2

 Before constructing a confidence interval for p, you should check some important conditions.  Random: If the sample isn’t random (using sound sampling techniques), inference about the larger population is NOT possible.  In addition to being random, samples must also involve chance – the 10% rule ensures that while keeping samples independent.  Large Counts condition ensures the sampling distribution is Normal.  What if one of the conditions is violated?  Not random  No inference about population possible  Not Normal  The Confidence interval will not likely capture the population proportion Conditions for Estimating p

 An AP Statistics class at a large high school conducts a survey. They ask the first 100 students to arrive at school one morning whether or not they slept at least 8 hours the night before. Only 17 students said “yes.”  A quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. Of the bags selected, 3 had too much salt. Checking Conditions

Constructing a Confidence Interval for p

Example

 State: What parameter do you want to estimate, and at what confidence level?  Plan: Identify the appropriate inference method. Check conditions.  Do: If the conditions are met, perform conditions  Conclude: Interpret your interval in the context of the problem.  Calculator instructions p in book. Four Step Process

Choosing a Sample Size

 In the company’s prior-year survey, 80% of customers surveyed said they were “somewhat satisfied” or “very satisfied.” Using this value, find the sample size needed for a margin of error of 3% at a 95% confidence level.  What if the company president demands a 99% confidence instead? Try it