1. Today Today: Chapter 12 Sections from Chapter 12: 12.1, 12.3-12.4 Recommended Questions:

2. Example: An insurance company want to know if the average speed at which men drive is greater than that of women drivers The company took a random sample of 22 cars driven by men on a highway and recorded the average speed of each driver The company took another random sample of 14 cars driven by women on the same highway and recorded the average speed of each driver How might you go about testing the hypothesis?

3. Inferences about Two Population Means (12.4) Situation: –Have 2 independent random samples –Each sample comes from a normal population –The population standard deviations are equal –Want to test test a hypothesis about the population means

4. Example (continued): The hypothesis we wish to test is:

5. Test Statistic: Where When H 0 is true, t has a t-distribution with (n 1 +n 2 - 2) degrees of freedom

6. Computing a P-Value P-Value depends on the alternative

7. Putting it all together Example: Insurance company wants to know if average speed at which men drive is greater than women drivers Company took a random sample of 22 cars driven by men on a highway and recorded the average speed of each driver They took another random sample of 14 cars driven by women on the same highway and recorded the average speed of each driver

8. Sample Statistics

9. Hypothesis: Test Statistic: P-Value:

10. Example: Gender Differences in Metered-Dose Inhaler-Spacer (MDI) Device Technique (Pharmacotherapy, 2000) Asthma is a disease of chronic airway inflamation A typical treatment for asthma is using inhaled formulations (e.g., corticosteroids) Proper usage consists of shaking the inhaler, slowly depressing the cannister and simultaneously inhaling over 3-5 seconds and then holding in the breath for 10 seconds Study in 1990’s indicated gender differences in the usage of the MDI

11. Example: Study performed to determine whether gender affects the correct use of MDI device 83 3 rd year Doctor of Pharmacy students (31 men; 52 women) were given a placeobo MSI and 20 minutes training on the device One week later, the students returned and were tested on their ability to use the device…each student was assigned a score in usage by the tester Mean score for males was 8.68 and mean score for women was 8.65 with sample standard deviations of 3.62 and 4.00 respectively What do these data indicate?

12. Example: As the U.S.-led war with Iraq moves into its third week, so does the media coverage of the war on every major outlet. Professional media critics have weighed in with their opinions, but just what does the American public think of the news coverage of the war so far? The latest CNN/USA Today/Gallup poll, conducted March 29-30, asked Americans just that question.

13. Example: The results show that Americans, in general, rate the media positively. Still, there has been a sharp decrease in the percentage of Americans who rate the media coverage as "excellent" since the start of the war. The March 29-30 poll asked Americans to rate the job news organizations in this country have done in covering the war with Iraq. Overall, 38% of Americans say the news media are doing an excellent job in reporting on the war These are generally positive results, but over the past week there has been significant change in the willingness of Americans to rate coverage of the war at the top end of the scale. At the start of the war, a significantly higher 46% of Americans said the news media were doing an excellent job covering the war, 8 percentage points higher than the current rating. Is there really evidence that public opinion has shifted?

14. Comparing Proportions (12.3) Situation: –Have 2 independent random samples –Each sample comes from a Bernoulli population –Want to test test a hypothesis about the equality of the population proportions

15. Example (continued): The hypothesis we wish to test is:

16. Test Statistic: Where When H 0 is true, Z has a standard normal distribution

17. Computing a P-Value P-Value depends on the alternative

18. Putting it all together Example: The March 29-30 poll asked Americans to rate the job news organizations in this country have done in covering the war with Iraq. Overall, 38% of Americans say the news media are doing an excellent job in reporting on the war These are generally positive results, but over the past week there has been significant change in the willingness of Americans to rate coverage of the war at the top end of the scale. At the start of the war, a significantly higher 46% of Americans said the news media were doing an excellent job covering the war, 8 percentage points higher than the current rating. The sample size in both cases was 1012 adults Is there really evidence that public opinion has shifted?

19. Hypothesis: Test Statistic: P-Value: