Chapter 10 Inference on Two Samples 10.3 Inference About Two Population Proportions

Step 1. A claim is made regarding two population proportions. The claim is used to determine the null and alternative hypothesis. The hypothesis can be structured in one of three ways. NOTE: p 1 is the assumed value of the population proportion for population 1 and p 2 is the assumed value of the population proportion for population 2.

Step 4: Compare the critical value with the test statistic:

Step 5: State the conclusion.

EXAMPLEFinding a Confidence Interval for the Difference between Two Population Proportions An economist obtains a random sample of 800 urban households and finds that 338 of them have Internet access. He obtains a random sample of 750 rural households and finds that 292 of them have Internet access. Find a 99% confidence interval for the difference between the proportion of urban households that have Internet access and the proportion of rural households that have Internet access.

EXAMPLE Determining Sample Size A doctor wants to estimate the difference in the proportion of year old mothers that received prenatal care and the proportion of year old mothers that received prenatal care. What sample size should be obtained if she wishes the estimate to be within 2 percentage points with 95% confidence assuming (a) she uses the results of the National Vital Statistics Report results in which 98.0% of year old mothers received prenatal care and 99.2% of year old mothers received prenatal care. (b) she does not use any prior estimates.