Which of the popular two drugs – Lipitor or Pravachol – helps lower “bad cholesterol” more? 4000 people with heart disease were randomly selected to be placed in one of the two groups. At the end of the study the subjects in the Lipitor group had an average of 62 milligrams of “bad cholesterol” per deciliter of blood and the subjects in the Pravachol group had and average of 95 milligrams of “bad cholesterol” per deciliter of blood.
Who is more likely to binge drink: male or female college students Who is more likely to binge drink: male or female college students? The Harvard School of Public Health surveys random samples of male and female undergraduate students at four-year colleges and universities about their drinking behaviors. AP Statistics, Section 11.2
Section 11.2 Comparing Two Means AP Statistics March 11, 2011
AP Statistics, Section 11.2
1 x1 n1 s1 2 x2 n2 s2 Statistics Parameters Population Variable Mean Standard Deviation Sample Size 1 x1 n1 s1 2 x2 n2 s2 AP Statistics, Section 11.2
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 African American men. Such observational studies do not establish causation. Researchers therefore designed a randomized comparative experiment. AP Statistics, Section 11.2
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. AP Statistics, Section 11.2
Example Group 1 (Calcium) results: Group 2 (Placebo) 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 AP Statistics, Section 11.2
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 H0: µ1= µ2 (There is no difference in the blood pressure changes) Ha: µ1> µ2 (The men taking calcium see a larger decrease in blood pressure) AP Statistics, Section 11.2
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. (2-Sample T-Test) Independent? Because of randomization, we are willing to regard the calcium and placebo groups as independent samples. We are not sampling without replacement from a population. Normal? Use Normal Probability Plots to check for normality. The book says “no departures from normality” AP Statistics, Section 11.2
Graphs appear to be somewhat linear, which tells us there is no reason to believe the distribution is not approximately normal. AP Statistics, Section 11.2
AP Statistics, Section 11.2
AP Statistics, Section 11.2
Example Step 3: Compute the test statistic and the P-value. Remember the P-value is also dependent on the degrees of freedom. AP Statistics, Section 11.2
AP Statistics, Section 11.2
AP Statistics, Section 11.2
AP Statistics, Section 11.2
AP Statistics, Section 11.2
We would fail to reject the Null Hypothesis. Step 4: Interpretaion: We would fail to reject the Null Hypothesis. The experiment provides some evidence that calcium reduces blood pressure, but the evidence is not significant enough at the 5% level of significance. AP Statistics, Section 11.2
Exercises 11.37-11.49 odd, 11.53-11.73 odd AP Statistics, Section 11.2