1. Section 11.2 Comparing Two Means AP Statistics Winter 2006

2. AP Statistics, Section 11.22 Conditions for Comparing Two Means We have two SRSs, from two distinct populations. The samples are independent. That is, one sample has no influence on the other. Matching violates independence, for example. We measure the same variable for both samples. Both populations are normally distributed. The means and standard deviations of the populations are unknown.

3. AP Statistics, Section 11.23 Example Does increasing the amount of calcium in our diet reduce blood pressure? Examination of a large sample of people revealed a relationship between calcium intake and blood pressure. The relationship was strongest for black men. Such observational studies do not establish causation. Researchers therefore designed a randomized comparative experiment.

4. AP Statistics, Section 11.24 Example The subjects in part of the experiment were 21 healthy black men. A randomly chosen group of 10 of the men received a calcium supplement for 12 weeks. The group of 11 men received a placebo pill that looked identical. The experiment was double-blind. The response variable is the decrease in systolic (heart contracted) blood pressure for a subject after 12 weeks, in millimeters of mercury. An increase appears as a negative response.

5. AP Statistics, Section 11.25 Example Group 1 (Calcium) results:  7, -4, 18, 17, -3, -5, 1, 10, 11, -2  n=10, x-bar=5.000, s=8.743 Group 2 (Placebo) results:  -1, 12, -1, -3, 3, -5, 5, 2, -11, -1, -3  n=11, x-bar=-0.273, s=5.901

6. AP Statistics, Section 11.26 Inference Tool Box Step 1: Identify the popluation(s) of interest and the parameter(s) you want to draw conclusions about. State hypothesis in words and symbols.  Population of interest: Men  Parameter: Differences in blood pressure  H 0 : µ 1 = µ 2 (There is no difference in the blood pressure changes)  H a : µ 1 > µ 2 (The men taking calcium see a larger decrease in blood pressure)

7. AP Statistics, Section 11.27 Inference Tool Box Step 2: Choose the appropriate inference procedure, and verify the conditions for using the selected procedure.  Test? Because we don’t know the population standard deviation, we’ll use a t test. Since we’re not comparing a person with himself, we have two sample.  Independent? SRSs, therefore independent.  Normal? Use back-to-back stemplots to check for normality. The book says “no departures from normality”

8. AP Statistics, Section 11.28 Inference Tool Box Step 3: Compute the test statistic and and the P- value.  Test? Because we don’t know the population standard deviation, we’ll use a t test. Since we’re not comparing a person with himself, we have two sample.  Independent? SRSs, therefore independent.  Normal? Use back-to-back stemplots to check for normality. The book says “no departures from normality”

9. AP Statistics, Section 11.29 Example Step 3: Compute the test statistic and the P-value. Remember the P- value is also dependent on the degrees of freedom.

10. AP Statistics, Section 11.210 Exercises 11.37-11.49 odd, 11.53-11.73 odd