Chapter 10, part D

IV. Inferences about differences between two population proportions You will have two population proportions, p1 and p2. The true difference, (p1-p2), is unknown so you take the difference between sample mean proportions as point estimators.

A. Sampling Distribution If n1p1, p1(1-p1), n2p2, n2(1-p2) are ALL  5, we can approximate the sampling distribution with the normal probability distribution.

B. Interval Estimation Interpretation for this confidence interval is the same as before. And since it’s very unlikely that we know the population proportions, you can use the samples to calculate the standard error.

An Example Problem #33 in the text book. Let p1 be the proportion of women in favor of banning the sale of alcohol and p2 is the proportion of men who favor the same. Sample statistics: 25% of 496 women sampled, and 16 % of 505 men, believe in the alcohol ban.

The Confidence Interval Calculating the 95% confidence interval begins with calculating the standard error. ( )  1.96(.0254) or a range between.0402 and.1398

C. Hypothesis Tests about (p1-p2) One example of a hypothesis test might be whether white workers and non-white workers have any difference in their preference for union membership. Ho: p1-p2 = 0 Ha: p1-p2  0

One modification The author’s suggest that if you set up a hypothesis where the proportions are hypothesized to be the same, to combine (pool) the samples to provide one estimate, p-bar. So then you use this in the calculation of the standard error.

An example In a sample of 80 minority workers, 20% claim to be a union member. 16% of a sample of 100 white workers are union members. Test at 90% confidence if these proportions are different. H0: p1-p2=0 Ha: p1-p2  0

=.1778 =.0574 Z=(.04-0)/.0574 = Fail to reject the Ho, and claim that there is no difference in proportion of union membership between whites and non-whites.