1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley AP Statistics Objectives Ch22

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley  Be able to write a conclusion for a 2-proportion interval  Be able to pool two sample proportions to create one pooled proportion  Be able to write a conclusion for a 2-proportion significance test AP Statistics Objectives Ch22

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley  Variance of independent random variables add  Sampling distribution of the difference between two proportions  Two-proportion z-interval  Pooling  Two-proportion z-test Vocabulary

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Classroom Notes Chapter 22 Assignments Chapter 22 Answers 2-proportion z-interval example 1 2-proportion z-interval example 2 2-proportion z-test example 1

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 5 Chapter 22 Assignments Part I Pages 508-509 #4,12,14,16 Part II Pages 510-511 #20,21&22, 24, 26

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 6 Comparing Two Proportions 1. We often want to know how two groups differ. Is a treatment better than a placebo? Is this year’s results better than last year’s?

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 7 Another Ruler 2. Recall: Pythagorean Theorem of Stats? We don’t add standard deviations. Instead we add the standard deviation squares… called variance. Also remember that we always add variances, we can’t take it out.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 8 Another Ruler

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 9 The Standard Deviation of the Difference Between Two Proportions 4. Proportions observed in independent random samples are independent. Thus, we can add their variances. So… The standard deviation of the difference between two sample proportions is Thus, the standard error is

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 10 Assumptions and Conditions 5. Independence Assumptions: Randomization Condition: The data in each group should be drawn independently and at random from a homogeneous population or generated by a randomized comparative experiment. The 10% Condition: If the data are sampled without replacement, each sample should not exceed 10% of the their population. Independent Groups Assumption: The two groups we’re comparing must be independent of each other. 6. Large Enough Sample Assumption: Success/Failure Condition: Both groups are big enough that at least 10 successes and at least 10 failures have been observed in each.

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 11 The Sampling Distribution 7. We already know that for large enough samples, each of our proportions has an approximately Normal sampling distribution. The same is true of their difference.

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 12 The Sampling Distribution (cont.) 8. Provided that the sampled values are independent, the samples are independent, and the samples sizes are large enough, the sampling distribution of is modeled by a Normal model with Mean: Standard deviation:

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 13 Two-Proportion z-Interval 9. When the conditions are met, we are ready to find the confidence interval for the difference of two proportions: The confidence interval is where The critical value,z*, depends on the particular confidence level, C, that you specify.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Proportion z-Interval Slide 22- 14 10. There has been debate among doctors whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery, 16 eventually died of prostate cancer, compared with 31 of the 348 who did not have surgery.

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 15 10. There has been debate among doctors whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery, 16 eventually died of prostate cancer, compared with 31 of the 348 who did not have surgery. Create a 95% confidence interval for the difference in rates of death for the two groups.

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 16 10. There has been debate among doctors whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery, 16 eventually died of prostate cancer, compared with 31 of the 348 who did not have surgery. Create a 95% confidence interval for the difference in rates of death for the two groups. Sample values are reasonably independent, because Randomization Condition: The men in this EXPERIMENT were randomly assigned treatments of surgery or no surgery. The 10% Condition: The 347 men who had surgery and the 348 men who did not have surgery are both less than 10% of all men with prostrate cancer.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 17 10. There has been debate among doctors whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery, 16 eventually died of prostate cancer, compared with 31 of the 348 who did not have surgery. Create a 95% confidence interval for the difference in rates of death for the two groups.

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 18 10. There has been debate among doctors whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery, 16 eventually died of prostate cancer, compared with 31 of the 348 who did not have surgery. Create a 95% confidence interval for the difference in rates of death for the two groups. Since all conditions are satisfied, we will perform a 2-proportion z-interval.

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 19 10. There has been debate among doctors whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery, 16 eventually died of prostate cancer, compared with 31 of the 348 who did not have surgery. Create a 95% confidence interval for the difference in rates of death for the two groups.

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 20 10. There has been debate among doctors whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery, 16 eventually died of prostate cancer, compared with 31 of the 348 who did not have surgery. Create a 95% confidence interval for the difference in rates of death for the two groups. (0.006, 0.080)

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 21 10. There has been debate among doctors whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery, 16 eventually died of prostate cancer, compared with 31 of the 348 who did not have surgery. Create a 95% confidence interval for the difference in rates of death for the two groups. We are 95% confident that the proportion of male patients who die from prostate cancer after having no surgery is between 0.58% and 8.02% higher than the proportion of patients who die after having surgery. (.0058,.0802)

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Proportion z-Interval Slide 22- 22 11. The Centers for Disease Control report a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease.

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Proportion z-Interval Slide 22- 23 11. The Centers for Disease Control report a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease.

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 24 Randomization Condition: American men and women age 65 and older were selected randomly. The 10% Condition: 1012 men and 1062 women are less than 10% of all senior men and women. 11. The Centers for Disease Control report a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease. Sample values are reasonably independent, because Independent Groups: The sample of senior men and the sample of senior women were selected independently from each other.

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 25 11. The Centers for Disease Control report a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease.

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 26 11. The Centers for Disease Control report a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease. Since all conditions are satisfied, we will perform a 2-proportion z-interval.

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 27 11. The Centers for Disease Control report a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease.

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 28 (.055,.141) 11. The Centers for Disease Control report a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease.

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 29 I am 95% confident that the proportion of American women age 65 and older who suffer from arthritis is between 5.5% and 14.0% higher than the proportion of American men the same age who suffer from arthritis. (.055,.0141) 11. The Centers for Disease Control report a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease.

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 30 Two-Proportion z-Test 1. The typical hypothesis test for the difference in two proportions is the one of no difference. In symbols, H 0 : p 1 – p 2 = 0 Since we assume the null hypothesis is true, that means that the standard deviations for each proportion are the same. When the standard deviations of two samples are the same, we combine (pool) the counts to get one overall proportion.

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 31 Two-Proportion z-Test (cont.) 2. The pooled proportion is where and If the numbers of successes are not whole numbers, round them first. (This is the only time you should round values in the middle of a calculation.)

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 32 Two-Proportion z-Test (cont.) 3. We then put this pooled value into the formula, substituting it for both sample proportions in the standard error formula:

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 33 Two-Proportion z-Test 4. The conditions for the two-proportion z-test are the same as for the two-proportion z-interval. We are testing the hypothesis H 0 : p 1 - p 2 = 0. Now we find the test statistic:

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 34 Two-Proportion z-Test (cont.) 5. When the conditions are met and the null hypothesis is true, this statistic follows the standard Normal model, so we can use that model to obtain a P-value.

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 35 What Can Go Wrong? 6. Don’t use two-sample proportion methods when the samples aren’t independent. These methods give wrong answers when the independence assumption is violated. Don’t apply inference methods when there was no randomization. Our data must come from representative random samples or from a properly randomized experiment.

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 36 What have we learned? 7. Perhaps the most important thing to remember is that the concepts and interpretations are essentially the same—only the mechanics have changed slightly.

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 37 What have we learned? 8. Hypothesis tests and confidence intervals for the difference in two proportions are based on Normal models. Both require us to find the standard error of the difference in two proportions. We do that by adding the variances of the two sample proportions, assuming our two groups are independent. When we test a hypothesis that the two proportions are equal, we pool the sample data; for confidence intervals we don’t pool.

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 38 9. A Vermont study published in December 2001 by the American Academy of Pediatrics examined parental influence on teenagers’ decisions to smoke. A group of students who had never smoke were questioned about their parents’ attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking?

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 39 9. A Vermont study published in December 2001 by the American Academy of Pediatrics examined parental influence on teenagers’ decisions to smoke. A group of students who had never smoke were questioned about their parents’ attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? PHANTOMS Parameter of Interest

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 40 9. A Vermont study published in December 2001 by the American Academy of Pediatrics examined parental influence on teenagers’ decisions to smoke. A group of students who had never smoke were questioned about their parents’ attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? Remember: PHANTOMS Hypotheses

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 41 9. …..These students were questioned again two years later to see if they had started smoking. The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? Remember: PHANTOMS Assumptions & Conditions Sample values can be considered independent, because

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 42 9. A Vermont study published in December 2001 by the American Academy of Pediatrics examined parental influence on teenagers’ decisions to smoke. A group of students who had never smoke were questioned about their parents’ attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? Remember: PHANTOMS Assumptions

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 43 9. A Vermont study published in December 2001 by the American Academy of Pediatrics examined parental influence on teenagers’ decisions to smoke. A group of students who had never smoke were questioned about their parents’ attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? Remember: PHANTOMS Name the test Because the conditions are satisfied, I will use a two-proportion z-test.

44. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 44 9. A Vermont study published in December 2001 by the American Academy of Pediatrics examined parental influence on teenagers’ decisions to smoke. A group of students who had never smoke were questioned about their parents’ attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? Remember: PHANTOMS Test statistic

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 45 9. …The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? Remember: PHANTOMS Test statistic 0.0668

46. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 46 9. …The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? Remember: PHANTOMS Test statistic

47. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 47 9. A Vermont study published in December 2001 by the American Academy of Pediatrics examined parental influence on teenagers’ decisions to smoke. A group of students who had never smoke were questioned about their parents’ attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? Remember: PHANTOMS Obtain P-value P-value = 2 P(z > 1.168)

48. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 48 9. …The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? Remember: PHANTOMS Make a decision We fail to reject the null hypothesis.

49. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 49 9. A Vermont study published in December 2001 by the American Academy of Pediatrics examined parental influence on teenagers’ decisions to smoke. A group of students who had never smoke were questioned about their parents’ attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that among 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among 41 students who initially said their parents were lenient about smoking, 11 became smokers. Do these data provide strong evidence that parental attitude influences teenagers’ decisions about smoking? PHANTOMS State the conclusion in context There is not enough evidence to conclude that parental attitudes toward smoking influences a teen’s decision to smoke.

50. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 50 10. Interpret the P-value There is a 24.3% chance that if there is no difference between the proportion of teens that smoke for parents that are lenient about smoking and parents that that disapprove of smoking, then there could be a 7.8% or smaller difference due to sample error (variance). P-value = 2 P(z > 1.168)

51. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 51 10. Interpret the P-value There is a 24.3% chance that if there is no difference between the proportion of teens that smoke for parents that are lenient about smoking and parents that that disapprove of smoking, then there could be a 7.8% or smaller difference due to sample error (variance). P-value = 2 P(z > 1.168)

52. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Questions Slide 22- 52 Pages 508-509 #4,12 Page 509 #14,16 Page 510 #20,21,22 Pages 510-511 #24,26 Part I Part III 4 12 1416 20 21 22 24 26 Part II Part IV

53. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #4 Slide 22- 53 4. In October 2000 the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that they had high school diplomas.

54. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #4 Slide 22- 54 4. In October 2000 the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that they had high school diplomas. a) Are the assumptions and conditions necessary for inference satisfied? Explain. Independence between the respondents within each group is reasonable, because the male and female respondents could be representative of all males and females age 24 respectfully and 12,460 is less than 10% of all males age 24 and 12,678 is less than 10% of all females age 24. The sample of males and the sample of females were collected independent of each other.

55. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #4 Slide 22- 55 4. In October 2000 the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that they had high school diplomas. a) Are the assumptions and conditions necessary for inference satisfied? Explain. 12,460(.849) = 10,578.5 males graduated and 1881.5 didn’t. Both are at least 10. 12,678(.881) = 11,169.3 females graduated and 1508.7 didn’t. Both are at least 10. So both samples are reasonably large enough. Since the conditions have been met, we can create a two-proportion z-interval.

56. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #4 Slide 22- 56 4. In October 2000 the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that they had high school diplomas. b) Created a 95% confidence interval for the difference in graduation rates between males and females.

57. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #4 Slide 22- 57 4. In October 2000 the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that they had high school diplomas. b) Created a 95% confidence interval for the difference in graduation rates between males and females. = 0.032 (.024,.04)

58. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #4 Slide 22- 58 4. In October 2000 the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that they had high school diplomas. c) Interpret your confidence interval.

59. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #4 Slide 22- 59 4. In October 2000 the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that they had high school diplomas. d) Does this provide strong evidence that girls are more likely than boys to complete high school? Explain.

60. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #4 Slide 22- 60 4. In October 2000 the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that they had high school diplomas. d) Does this provide strong evidence that girls are more likely than boys to complete high school? Explain.

61. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 61 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones?

62. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 62 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? a) What kind of design was used to collect these data?

63. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 63 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? b) Write appropriate hypotheses.

64. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 64 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? c) Are the assumptions and conditions necessary for inference satisfied? Independence between the cardiac patients within each group is reasonable, because Depression group: these patients could be representative of all cardiac patients with depression and 89 is less than 10% of all such patients. No Depression group: these patients could be representative of all cardiac patients w/o depression and 361 is less than 10% of all such patients.

65. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 65 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? c) Are the assumptions and conditions necessary for inference satisfied? Both groups are independent of each other. Depressed: 26 died and 63 didn’t. Both are > 10. Not Depressed: 67 died and 294 didn’t. Both are > 10. So both samples are reasonably large enough. Since the conditions have been met, we can create a two-proportion z-test.

66. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 66 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? d) Test the hypothesis and state your conclusion.

67. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 67 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? d) Test the hypothesis and state your conclusion. -2.2234 0.0131

68. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 68 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? d) Test the hypothesis and state your conclusion.

69. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 69 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? e) Explain in this context what your P-value means.

70. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 70 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? f) If your conclusion is actually incorrect, which type of error did you commit?

71. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #12 Slide 22- 71 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? f) If your conclusion is actually incorrect, which type of error did you commit?

72. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #14 Slide 22- 72 14. Consider again the study of the association between depression and cardiac disease survivability in Exercise 12. 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones?

73. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #14 Slide 22- 73 14. Consider again the study of the association between depression and cardiac disease survivability in Exercise 12. 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? a) Create a 95% confidence interval for the difference in survival rates.

74. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #14 Slide 22- 74 14. Consider again the study of the association between depression and cardiac disease survivability in Exercise 12. 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? a) Create a 95% confidence interval for the difference in survival rates. Depression group: These patients could be representative of all cardiac patients with depression and 89 of these patients is less than 10% of all such patients. No Depression group: These patients could be representative of all cardiac patients w/o depression and 361 of these patients is less than 10% of all such patients. Sample values can be considered independent, because

75. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #14 Slide 22- 75 14. Consider again the study of the association between depression and cardiac disease survivability in Exercise 12. 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? a) Create a 95% confidence interval for the difference in survival rates.

76. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 76 14. Consider again the study of the association between depression and cardiac disease survivability in Exercise 12. 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? a) Create a 95% confidence interval for the difference in survival rates. Since all conditions are satisfied, we will preform a 2-proportion z-interval.

77. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 22- 77 14. Consider again the study of the association between depression and cardiac disease survivability in Exercise 12. 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? a) Create a 95% confidence interval for the difference in survival rates. (.004,.209)

78. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #14 Slide 22- 78 14. Consider again the study of the association between depression and cardiac disease survivability in Exercise 12. 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? b) Interpret your interval in this context.

79. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #14 Slide 22- 79 14. Consider again the study of the association between depression and cardiac disease survivability in Exercise 12. 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? c) Carefully explain what “95% confidence” means.

80. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #14 Slide 22- 80 14. Consider again the study of the association between depression and cardiac disease survivability in Exercise 12. 12. A study published in the Archives of General Psychiatry in March 2001examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? c) Carefully explain what “95% confidence” means.

81. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #16 Slide 22- 81 16. In 2003 the Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York’s Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy doses of soot and ash on September 11 were classified as having low birthweight. Only 4% of 2300 babies born in another New York City hospital whose mothers had not been near the site of the disaster were similarly classified. Does this indicate a possibility that air pollution might be linked to a significantly higher proportion of low weight babies?

82. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #16 Slide 22- 82 16. In 2003 the Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York’s Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy doses of soot and ash on September 11 were classified as having low birthweight. Only 4% of 2300 babies born in another New York City hospital whose mothers had not been near the site of the disaster were similarly classified. Does this indicate a possibility that air pollution might be linked to a significantly higher proportion of low weight babies? a) Test an appropriate hypothesis and state your conclusion.

83. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #16 Slide 22- 83 16. In 2003 the Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York’s Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy doses of soot and ash on September 11 were classified as having low birthweight. Only 4% of 2300 babies born in another New York City hospital whose mothers had not been near the site of the disaster were similarly classified. Does this indicate a possibility that air pollution might be linked to a significantly higher proportion of low weight babies? a) Test an appropriate hypothesis and state your conclusion. 9/11 Soot group: These babies could be representative of all babies born to mothers exposed to large amounts of air pollution and 182 of these babies is less than 10% of all such babies. Not Soot group: These babies could be representative of all babies born to mothers not exposed to large amounts of air pollution and 2300 of these patients is less than 10% of all such babies. Sample values can be considered independent, because

84. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #16 Slide 22- 84 16. In 2003 the Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York’s Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy doses of soot and ash on September 11 were classified as having low birthweight. Only 4% of 2300 babies born in another New York City hospital whose mothers had not been near the site of the disaster were similarly classified. Does this indicate a possibility that air pollution might be linked to a significantly higher proportion of low weight babies? a) Test an appropriate hypothesis and state your conclusion.

85. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #16 Slide 22- 85 16. In 2003 the Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York’s Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy doses of soot and ash on September 11 were classified as having low birthweight. Only 4% of 2300 babies born in another New York City hospital whose mothers had not been near the site of the disaster were similarly classified. Does this indicate a possibility that air pollution might be linked to a significantly higher proportion of low weight babies? a) Test an appropriate hypothesis and state your conclusion.

86. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #16 Slide 22- 86 16. In 2003 the Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York’s Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy doses of soot and ash on September 11 were classified as having low birthweight. Only 4% of 2300 babies born in another New York City hospital whose mothers had not been near the site of the disaster were similarly classified. Does this indicate a possibility that air pollution might be linked to a significantly higher proportion of low weight babies? b) If you concluded there is a difference, estimate that difference with a confidence interval and interpret that interval in context.

87. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part I #16 Slide 22- 87 16. In 2003 the Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York’s Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy doses of soot and ash on September 11 were classified as having low birthweight. Only 4% of 2300 babies born in another New York City hospital whose mothers had not been near the site of the disaster were similarly classified. Does this indicate a possibility that air pollution might be linked to a significantly higher proportion of low weight babies? b) If you concluded there is a difference, estimate that difference with a confidence interval and interpret that interval in context.

88. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #20 Slide 22- 88 20. A survey of 430 randomly chosen adults found that 21% of the 222 men and 18% of the 208 women had purchased books online.

89. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #20 Slide 22- 89 20. A survey of 430 randomly chosen adults found that 21% of the 222 men and 18% of the 208 women had purchased books online. a) Is there evidence that men are more likely than women to make online purchases of books? Test an appropriate hypothesis and state your conclusion in context.

90. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #20 Slide 22- 90 20. A survey of 430 randomly chosen adults found that 21% of the 222 men and 18% of the 208 women had purchased books online. a) Is there evidence that men are more likely than women to make online purchases of books? Test an appropriate hypothesis and state your conclusion in context.

91. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #20 Slide 22- 91 20. A survey of 430 randomly chosen adults found that 21% of the 222 men and 18% of the 208 women had purchased books online. a) Is there evidence that men are more likely than women to make online purchases of books? Test an appropriate hypothesis and state your conclusion in context.

92. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #20 Slide 22- 92 20. A survey of 430 randomly chosen adults found that 21% of the 222 men and 18% of the 208 women had purchased books online. a) Is there evidence that men are more likely than women to make online purchases of books? Test an appropriate hypothesis and state your conclusion in context.

93. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #20 Slide 22- 93 20. A survey of 430 randomly chosen adults found that 21% of the 222 men and 18% of the 208 women had purchased books online. b) If your conclusion in fact proves to be wrong, did you make a Type I or Type II error?

94. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #20 Slide 22- 94 20. A survey of 430 randomly chosen adults found that 21% of the 222 men and 18% of the 208 women had purchased books online. b) If your conclusion in fact proves to be wrong, did you make a Type I or Type II error?

95. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #21 Slide 22- 95 21. It’s widely believed that regular mammogram screening may detect breast cancer early, resulting in fewer deaths from that disease. One study that investigated this issue over a period of 18 years was published during the 1970s. Among 30,565 women who had never had mammograms, 196 died of breast cancer, while only 153 of 30,131 who had undergone screening died of breast cancer.

96. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #21 Slide 22- 96 21. It’s widely believed that regular mammogram screening may detect breast cancer early, resulting in fewer deaths from that disease. One study that investigated this issue over a period of 18 years was published during the 1970s. Among 30,565 women who had never had mammograms, 196 died of breast cancer, while only 153 of 30,131 who had undergone screening died of breast cancer. a) Do these results suggest that mammograms may be an effective screening tool to reduce breast cancer deaths?

97. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #21 Slide 22- 97 21. It’s widely believed that regular mammogram screening may detect breast cancer early, resulting in fewer deaths from that disease. One study that investigated this issue over a period of 18 years was published during the 1970s. Among 30,565 women who had never had mammograms, 196 died of breast cancer, while only 153 of 30,131 who had undergone screening died of breast cancer. a) Do these results suggest that mammograms may be an effective screening tool to reduce breast cancer deaths?

98. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #21 Slide 22- 98 21. It’s widely believed that regular mammogram screening may detect breast cancer early, resulting in fewer deaths from that disease. One study that investigated this issue over a period of 18 years was published during the 1970s. Among 30,565 women who had never had mammograms, 196 died of breast cancer, while only 153 of 30,131 who had undergone screening died of breast cancer. a) Do these results suggest that mammograms may be an effective screening tool to reduce breast cancer deaths?

99. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #21 Slide 22- 99 21. It’s widely believed that regular mammogram screening may detect breast cancer early, resulting in fewer deaths from that disease. One study that investigated this issue over a period of 18 years was published during the 1970s. Among 30,565 women who had never had mammograms, 196 died of breast cancer, while only 153 of 30,131 who had undergone screening died of breast cancer. a) Do these results suggest that mammograms may be an effective screening tool to reduce breast cancer deaths?

100. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #21 Slide 22- 100 21. It’s widely believed that regular mammogram screening may detect breast cancer early, resulting in fewer deaths from that disease. One study that investigated this issue over a period of 18 years was published during the 1970s. Among 30,565 women who had never had mammograms, 196 died of breast cancer, while only 153 of 30,131 who had undergone screening died of breast cancer. b) If your conclusion is incorrect, what type of error have you committed?

101. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #21 Slide 22- 101 21. It’s widely believed that regular mammogram screening may detect breast cancer early, resulting in fewer deaths from that disease. One study that investigated this issue over a period of 18 years was published during the 1970s. Among 30,565 women who had never had mammograms, 196 died of breast cancer, while only 153 of 30,131 who had undergone screening died of breast cancer. b) If your conclusion is incorrect, what type of error have you committed?

102. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #22 Slide 22- 102 22. In 2001, the conclusion of the study outlined in Exercise 21 was questioned. A new 9-year study was conducted in Sweden, comparing 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared with 66 deaths among the control group. (New York Times, Dec 9, 2001)

103. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #22 Slide 22- 103 22. In 2001, the conclusion of the study outlined in Exercise 21 was questioned. A new 9-year study was conducted in Sweden, comparing 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared with 66 deaths among the control group. (New York Times, Dec 9, 2001) a) Do these results support the effectiveness of regular mammograms in preventing death from breast cancer?

104. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #22 Slide 22- 104 22. In 2001, the conclusion of the study outlined in Exercise 21 was questioned. A new 9-year study was conducted in Sweden, comparing 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared with 66 deaths among the control group. (New York Times, Dec 9, 2001) a) Do these results support the effectiveness of regular mammograms in preventing death from breast cancer?

105. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #22 Slide 22- 105 22. In 2001, the conclusion of the study outlined in Exercise 21 was questioned. A new 9-year study was conducted in Sweden, comparing 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared with 66 deaths among the control group. (New York Times, Dec 9, 2001) a) Do these results support the effectiveness of regular mammograms in preventing death from breast cancer?

106. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #22 Slide 22- 106 22. In 2001, the conclusion of the study outlined in Exercise 21 was questioned. A new 9-year study was conducted in Sweden, comparing 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared with 66 deaths among the control group. (New York Times, Dec 9, 2001) b) If your conclusion is incorrect, what kind of error have you committed?

107. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #22 Slide 22- 107 22. In 2001, the conclusion of the study outlined in Exercise 21 was questioned. A new 9-year study was conducted in Sweden, comparing 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared with 66 deaths among the control group. (New York Times, Dec 9, 2001) b) If your conclusion is incorrect, what kind of error have you committed?

108. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #24 Slide 22- 108 24. Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of the election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express support.

109. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #24 Slide 22- 109 24. Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of the election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express support. a) Write a 95% confidence interval for the percent of male voters who may vote for this candidate. Interpret your interval.

110. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #24 Slide 22- 110 24. Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of the election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express support. b) Write a 95% confidence interval for the percent of female voters who may vote for him. Interpret your interval.

111. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #24 Slide 22- 111 24. Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of the election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express support. c) Do the intervals for males and females overlap? What do you think this means about the gender gap?

112. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #24 Slide 22- 112 24. Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of the election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express support. d) Find a 95% confidence interval for the difference in the proportions of males and females who will vote for this candidate. Interpret your interval.

113. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #24 Slide 22- 113 24. Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of the election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express support. e) Does this interval contain zero? What does that mean?

114. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #24 Slide 22- 114 24. Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of the election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express support. f) Why do the results in parts c and e seem contradictory? If we want to see if there is a gender gap among voters with respect to this candidate, which is the correct approach? Why?

115. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #24 Slide 22- 115 24. Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of the election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express support. f) Why do the results in parts c and e seem contradictory? If we want to see if there is a gender gap among voters with respect to this candidate, which is the correct approach? Why?

116. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #26 Slide 22- 116 26. In August 2004, a Time magazine article about a survey of men’s attitudes reported that 11 of 161 black respondents and 20 of 358 Latino respondents responded “Yes” to the question “Are you a stay-at-home dad?” How big is the difference in proportions in the two populations?

117. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #26 Slide 22- 117 26. In August 2004, a Time magazine article about a survey of men’s attitudes reported that 11 of 161 black respondents and 20 of 358 Latino respondents responded “Yes” to the question “Are you a stay-at-home dad?” How big is the difference in proportions in the two populations? a) Construct and interpret an appropriate confidence interval.

118. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #26 Slide 22- 118 26. In August 2004, a Time magazine article about a survey of men’s attitudes reported that 11 of 161 black respondents and 20 of 358 Latino respondents responded “Yes” to the question “Are you a stay-at-home dad?” How big is the difference in proportions in the two populations? a) Construct and interpret an appropriate confidence interval.

119. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #26 Slide 22- 119 26. In August 2004, a Time magazine article about a survey of men’s attitudes reported that 11 of 161 black respondents and 20 of 358 Latino respondents responded “Yes” to the question “Are you a stay-at-home dad?” How big is the difference in proportions in the two populations?

120. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 22 Part II #26 Slide 22- 120 26. In August 2004, a Time magazine article about a survey of men’s attitudes reported that 11 of 161 black respondents and 20 of 358 Latino respondents responded “Yes” to the question “Are you a stay-at-home dad?” How big is the difference in proportions in the two populations?