1. Warm-up
An experiment on the side effects of pain relievers assigned arthritis patients to one of several over-the-counter pain medications. Of the 440 patients who took one brand of pain reliever, 23 suffered some “adverse symptom.” Does the experiment provide strong evidence that fewer than 10% of patients who take this medication have adverse symptoms?

2. Comparing Two Proportions
Section 10.2
Comparing Two Proportions

3. We’ve only just begun…
So far, we’ve studied inference for a population mean:
One sample z-procedures
One sample t-procedures
Matched pairs t-procedures
Two sample t-procedures
We’ve studied inference for a population proportion:
Next, we’ll examine two-sample inference for population proportions.

4. In my opinion…
The tricky part about inference is remembering the assumptions. Let’s review the assumptions for inference for a proportion.
Let’s look at how these would change for inference comparing TWO proportions.
We need to check both proportions:
Independent SRS’s
n1 and n2 times 10 has to be less than or equal to the population.
And… n(p1) and n(1-p1) for both samples have to be greater than or equal to 10.

5. Comparing Two Proportions
Two-Sample z Interval for p1 – p2
Two-Sample z Interval for a Difference Between Proportions
Comparing Two Proportions

6. Give it a shot!
To study the long-term effects of preschool programs for poor children, the High/Scope Educational Research Foundation has followed two groups of Michigan children since early childhood. One group of 62 children attended preschool as 3- and 4-year-olds. A control group of 61 children from the same area and similar backgrounds did not attend preschool.
The response variable of interest is the need for social services as adults. In the past ten years, 38 of the preschool sample and 49 of the control sample have needed social services. Give a 95% confidence interval for the difference in proportions between the two populations.

7. Pooled
When doing a proportions significance test H0: p1 = p2. In these instances we have to do a pooled sample proportion. Basically, you just take the total successes and divide by the total number in the samples. This is the pc you use in your standard deviation AND in your condition check.

8. Comparing Two Proportions
Significance Tests for p1 – p2
Comparing Two Proportions
If H0: p1 = p2 is true, the two parameters are the same. We call their common value p. But now we need a way to estimate p, so it makes sense to combine the data from the two samples. This pooled (or combined) sample proportion is:

9. Let’s go back to the preschool example.
Does the data indicate that the difference between the proportion of preschool children who need social services is less than the proportion of no-preschool children?

10. High levels of cholesterol in the blood are associated with higher risk of heart attacks. Will using a drug to lower blood cholesterol reduce heart attacks? The Helsinki Heart Study recruited middle-aged men with high cholesterol but no history of other serious medical problems to investigate this question. The volunteer subjects were assigned at random to one of two treatments: 2051 men took the drug gemfibrozil to reduce their cholesterol levels, and a control group of 2030 men took a placebo. During the next five years, 56 men in the gemfibrozil group and 84 men in the placebo group had heart attacks. Is the apparent benefit of gemfibrozil statistically significant? Perform an appropriate test to find out.

11. Homework
Chapter 10
# 14-18, 22, 23