1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley  Be able to identify the parameter of interest and write both Hypotheses for your test  Be able to check the appropriate conditions for a one-proportion z-test AP Statistics Objectives Ch20

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley  Be able to calculate the test statistic and P-value for your test  Know when to reject or fail to reject your null hypothesis  Be able to state the conclusion of your test in context AP Statistics Objectives Ch20

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley  Be able to interpret your P- value  Understand how to use PHANTOMS to preform a one-proportion z-test AP Statistics Objectives Ch20

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley  Null Hypothesis  Alternative Hypothesis  Two-sided alternative  One-sided alternative  P-value  One-proportion z-test Vocabulary

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Classroom Notes Chapter 20 Assignments Chapter 20 Answers

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 6 Chapter 20 Assignments Part I Pages 469-470 #2,4,11,12 Part II Pages 471-472 #14,18,24,26

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 7 Hypotheses 1. In Statistics, a hypothesis proposes a model for the world. Then we look at the data. Data consistent with the model lend support to the hypothesis, but do not prove it. Data inconsistent enough, can allow us to reject the model.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 8 Hypotheses (cont.) 2. Think about the logic of jury trials: To prove someone is guilty, we start by assuming they are innocent. We retain that hypothesis until the facts make it unlikely beyond a reasonable doubt. Then, and only then, we reject the hypothesis of innocence and declare the person guilty. If there is insufficient evidence to convict the defendant, the verdict isn’t “innocent”. It is “not guilty”.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 9 Hypotheses (cont.) 3. The same logic used in jury trials is used in statistical tests of hypotheses: We begin by assuming that a hypothesis is true. Next we consider whether the data are consistent with the hypothesis. If they are, all we can do is retain the hypothesis we started with. If they are not, then like a jury, we ask whether they are unlikely beyond a reasonable doubt.

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 10 Hypotheses (cont.)

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 11 Hypotheses (cont.) 6. A small P-value indicates that the observation is improbable for the proposed model, so we “reject the null hypothesis”. 7. A large P-value indicates the observation is in line with the proposed model, so we “fail to reject the null hypothesis”. Sometimes we say that the ”null hypothesis has been retained”. We never ”accept the null hypothesis”.

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 12 Testing Hypotheses 6. Null hypothesis, denoted H 0, specifies a population model parameter of interest and proposes a value for that parameter.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 13 A Trial as a Hypothesis Test (cont.) 7. Ultimately, we must make a decision. How unlikely is unlikely? Some people advocate setting rigid standards— 1 time out of 20 (0.05) or 1 time out of 100 (0.01). But if you have to make the decision, you must judge for yourself in any particular situation whether the probability is small enough to constitute “reasonable doubt.”

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 14 What to Do with an “Innocent” Defendant If the evidence is not strong enough to reject the presumption of innocent, the jury returns with a verdict of “not guilty.” The jury does not say that the defendant is innocent. All it says is that there is not enough evidence to convict, to reject innocence. The defendant may, in fact, be innocent, but the jury has no way to be sure.

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 15 What to Do with an “Innocent” Defendant (cont.) Said statistically, we will ” fail to reject the null hypothesis”. We never declare the null hypothesis to be true, because we simply do not know whether it’s true or not. Sometimes we say that the ”null hypothesis has been retained”.

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 16 What to Do with an “Innocent” Defendant (cont.) In a trial, the burden of proof is on the prosecution. In a hypothesis test, the burden of proof is on the unusual claim. The null hypothesis is the ordinary state of affairs, so it’s the alternative to the null hypothesis that we consider unusual (and for which we must marshal evidence).

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 17 PHANTOMS 8. There are four basic parts to a hypothesis test: 1. Hypotheses 2. Model 3. Mechanics 4. Conclusion P arameter of interest H ypotheses A ssumptions & Conditions N ame the test T est statistic O btain P-value M ake a decision S tate conclusion in context 8 Textbook

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 18 PHANTOMS

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 19 Alternative Alternatives A one-sided alternative focuses on deviations from the null hypothesis value in only one direction.

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 20 PHANTOMS 11. Assumptions & Conditions All models require assumptions, so state the assumptions and check any corresponding conditions.

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 19- 21 Assumptions and Conditions INDEPENDENCE ASSUMPTION Randomization Condition: An SRS or at least a sampling method that is not biased and that is representative of the population 10% Condition: If sampling without replacement, then the sample size, n, must be no larger than 10% of the population. Large Enough Sample Assumption

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 19- 22 Assumptions and Conditions LARGE ENOUGH SAMPLE ASSUMPTION Success/Failure Condition: We must expect at least 10 “successes” and at least 10 “failures.”

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 23 PHANTOMS 12. Name the test “Because the conditions are met, I will perform a one-proportion z-test.”

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 24 PHANTOMS

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 25 PHANTOMS 14. Obtain P-value The P-value is the conditional probability that the observed statistic value (or an even more extreme value) could occur if the null hypothesis is true Since this is a one-sample z-test, the test statistic is the z-score and the P-value is the probability of that z-score or more extreme.

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 26 P-value For two-sided alternatives, the P-value is the probability of deviating in either direction from the null hypothesis value. Use this if your z-score is negative Use this if your z-score is positive

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 27 P-value (cont.) For one-sided alternatives, the P-value is the probability of deviating in only the direction of the alternative - away from the null hypothesis value.

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 28 PHANTOMS

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 29 One-Proportion z-Test The conditions for the one-proportion z-test are the same as for the one proportion z-interval. We test the hypothesis H 0 : p = p 0 using the statistic where 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.

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 30 P-Values and Decisions: What to Tell About a Hypothesis Test How small should the P-value be in order for you to reject the null hypothesis? It turns out that our decision criterion is context- dependent. When we’re screening for a disease and want to be sure we treat all those who are sick, we may be willing to reject the null hypothesis of no disease with a fairly large P-value. A longstanding hypothesis, believed by many to be true, needs stronger evidence (and a correspondingly small P-value) to reject it. Another factor in choosing a P-value is the importance of the issue being tested.

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 31 P-Values and Decisions (cont.) Your conclusion about any null hypothesis should be accompanied by the P-value of the test. If possible, it should also include a confidence interval for the parameter of interest. Don’t just declare the null hypothesis rejected or not rejected. Report the P-value to show the strength of the evidence against the hypothesis. This will let each reader decide whether or not to reject the null hypothesis.

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 32 17. An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that 103 of 122 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline’s claim? Explain. Remember: PHANTOMS

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 33 17. An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that 103 of 122 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline’s claim? Explain. Remember: PHANTOMS P Parameter of Interest

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 34 17. An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that 103 of 122 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline’s claim? Explain. Remember: PHANTOMS H Hypotheses

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 35 17. An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that one 103 of 122 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline’s claim? Explain. Remember: PHANTOMS A It is reasonable to believe that the people surveyed were independent of each other, because the people surveyed could be representative of all air travelers for that airline (Randomization Condition) and 122 people would be less than 10% of all people using this airline (10% Condition). Assumptions and conditions

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 36 17. An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that one 103 of 122 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline’s claim? Explain. Remember: PHANTOMS Assumptions and conditions

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 37 17. An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that one 103 of 122 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline’s claim? Explain. Remember: PHANTOMS N Because the conditions are satisfied, we will use a one-proportion z-test. Name the test

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 38 17. An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that one 103 of 122 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline’s claim? Explain. Remember: PHANTOMS T est statistic

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 39 17. An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that 103 of 122 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline’s claim? Explain. Remember: PHANTOMS O P-value = P(z < -2.059) PHANTOMS M With a P-value this low, we reject the null hypothesis. btain the P-value ake a decision

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 40 An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that one 103 of 122 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline’s claim? Explain. Remember: PHANTOMS M If the airline returned lost luggage within 24 hours 90% of the time, we would expect to see the results found in this survey less than 2% of the time. We reject the null hypothesis. ake a decision

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 41 17. An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that one 103 of 122 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline’s claim? Explain. Remember: PHANTOMS S There is sufficient evidence to say that the proportion of lost luggage returned the next day is lower than the 90% claimed by the airline. tate the conclusion in context

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 42 *A Better Confidence Interval for Proportions To improve the CI method for Proportions: Take the original counts and add four phony observations, two to the successes and two to the failures. The adjusted confidence interval is: Note: y is the observed count & n is the sample size

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 43 *A Better Confidence Interval for Proportions (cont.) This adjusted form gives better performance overall and works much better for proportions near 0 or 1. It has the additional advantage that we no longer need to check the Success/Failure Condition. What conditions do need to be checked? Plausible Independence Condition, Randomization Condition, 10% Condition

44. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 44 What Can Go Wrong? Hypothesis tests are so widely used—and so widely misused—that the issues involved are addressed in their own chapter (Chapter 21). There are a few issues that we can talk about already, though:

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 45 18. What Can Go Wrong? Don’t base your null hypothesis on what you see in the data. You can reject the null hypothesis, but you can never “accept” or “prove” the null. Don’t forget to check the conditions.

46. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 46 What Can Go Wrong? (cont.) Don’t make your null hypothesis what you want to show to be true. You can reject the null hypothesis, but you can never “accept” or “prove” the null. Don’t forget to check the conditions. We need randomization, independence, and a sample that is large enough to justify the use of the Normal model.

47. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 47 19. What have we learned? A hypothesis test makes a yes/no decision about the plausibility of a parameter value. A confidence interval shows us the range of plausible values for the parameter.

48. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 48 #20. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contacts 420 randomly chosen adults, and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowls? Explain. Remember: PHANTOMS

49. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 49 20. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contacts 420 randomly chosen adults, and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowls? Explain. Remember: PHANTOMS Parameter of interest Let p be the proportion of adults that recognize the company brand name.

50. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 50 20. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contacts 420 randomly chosen adults, and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowls? Explain. Remember: PHANTOMS Hypotheses

51. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 51 20. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contacts 420 randomly chosen adults, and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowls? Explain. Remember: PHANTOMS Assumptions and conditions It is reasonable to believe that the adults contacted were independent of each other, because the adults contacted were randomly selected (Randomization Condition) and 420 adults would be less than 10% of all adults (10% Condition).

52. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 52 20. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contacts 420 randomly chosen adults, and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowls? Explain. Remember: PHANTOMS Assumptions and conditions

53. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 53 20. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contacts 420 randomly chosen adults, and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowls? Explain. Remember: PHANTOMS Name the test Because the conditions are satisfied, we will use a one-proportion z-test.

54. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 54 20. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contacts 420 randomly chosen adults, and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowls? Explain. Remember: PHANTOMS Test statistic

55. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 55 20. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contacts 420 randomly chosen adults, and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowls? Explain. Remember: PHANTOMS Obtain the P-value P-value = P(z > 1.297) Almost 10%, is this beyond reasonable doubt?

56. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 56 20. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contacts 420 randomly chosen adults, and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowls? Explain. Remember: PHANTOMS Make a decision With a P-value this high, I will fail to reject the null hypothesis.

57. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 57 20. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and associate it with computer equipment. The day after the game, a pollster contacts 420 randomly chosen adults, and finds that 181 of them know that this company manufactures printers. Would you recommend that the company continue to advertise during the Super Bowls? Explain. PHANTOMS State the conclusion in context There is insufficient evidence to claim that the proportion of adults that recognize the company’s brand name is greater than 40%. The observed 43% could be due to sampling error (variability). We would not recommend continuing to pay for Super Bowl advertising.

58. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Accurate Globe for $1? Slide 20- 58 Let’s gather data first.

59. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Is the true proportion of water under represented on the inflatable globes? Slide 20- 59

60. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 60 Independence is reasonable, because the points on the globe were chosen at random and _____ points on the globe is less than 10% of all points on the globe. We expect (.7)( ) = ________ points in the sample to be on water and _______ points not to be on water. Since both are at least 10, the sample is reasonably large enough. Is the true proportion of water under represented on the inflatable globes?

61. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 61 Since the conditions are met, we will use a one-proportion z-test. Is the true proportion of water under represented on the inflatable globes?

62. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 62 Is the true proportion of water under represented on the inflatable globes?

63. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 63 Is the true proportion of water under represented on the inflatable globes? With a P-value this small, we will reject the null hypothesis. With a P-value this large, we will fail to reject the null hypothesis.

64. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 20- 64 Is the true proportion of water under represented on the inflatable globes? There is insufficient evidence to say that the proportion of water is less than 70% on the inflatable globes. There is sufficient evidence to say that the proportion of water is less than 70% on the inflatable globes, so the water is under represented.

65. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More One-proportion z-tests Slide 20- 65 1. In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults drink milk. A regional farmers’ organization planning a new marketing campaign across its multi-county area polls a random sample of 750 adults living there. In this sample, 657 people said that they drink milk. Do these responses provide strong evidence that the 90% figure is not accurate for this region? Test an appropriate hypothesis and state your conclusion.

66. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More One-proportion z-tests Slide 20- 66 1. In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults drink milk. A regional farmers’ organization planning a new marketing campaign across its multi-county area polls a random sample of 750 adults living there. In this sample, 657 people said that they drink milk. Do these responses provide strong evidence that the 90% figure is not accurate for this region? Test an appropriate hypothesis and state your conclusion.

67. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More One-proportion z-tests Slide 20- 67 1. In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults drink milk. A regional farmers’ organization planning a new marketing campaign across its multi-county area polls a random sample of 750 adults living there. In this sample, 657 people said that they drink milk. Do these responses provide strong evidence that the 90% figure is not accurate for this region? Test an appropriate hypothesis and state your conclusion. Independence is reasonable, because a random sample was used and 750 adults is probably less than 10% of all adults in the region. We expect to find (750)(.9)= 675 adults that drink milk and 75 that don’t. Since both are at least 10, the sample is reasonably large enough.

68. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More One-proportion z-tests Slide 20- 68 1. In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults drink milk. A regional farmers’ organization planning a new marketing campaign across its multi-county area polls a random sample of 750 adults living there. In this sample, 657 people said that they drink milk. Do these responses provide strong evidence that the 90% figure is not accurate for this region? Test an appropriate hypothesis and state your conclusion. Since the conditions are met, we will create a one-proportion z-test.

69. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More One-proportion z-tests Slide 20- 69 1. In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults drink milk. A regional farmers’ organization planning a new marketing campaign across its multi-county area polls a random sample of 750 adults living there. In this sample, 657 people said that they drink milk. Do these responses provide strong evidence that the 90% figure is not accurate for this region? Test an appropriate hypothesis and state your conclusion.

70. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More One-proportion z-tests Slide 20- 70 1. In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults drink milk. A regional farmers’ organization planning a new marketing campaign across its multi-county area polls a random sample of 750 adults living there. In this sample, 657 people said that they drink milk. Do these responses provide strong evidence that the 90% figure is not accurate for this region? Test an appropriate hypothesis and state your conclusion. With a P-value this small, we will reject the null hypothesis.

71. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More One-proportion z-tests Slide 20- 71 1. In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults drink milk. A regional farmers’ organization planning a new marketing campaign across its multi-county area polls a random sample of 750 adults living there. In this sample, 657 people said that they drink milk. Do these responses provide strong evidence that the 90% figure is not accurate for this region? Test an appropriate hypothesis and state your conclusion. There is sufficient evidence to say that the true proportion of adults that drink milk in this region is not 90%. It appears to be smaller than 90% in this region.

72. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More One-proportion z-tests Slide 20- 72 2. In 2008 the distribution of yellow milk chocolate M&M’s was reported to be 14%. Mike believes that this is still true. Use your group sample to test an appropriate hypothesis and state your conclusion. Own your own.

73. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley M&M’s OPENED and COUNTED Slide 19- 73 Brown90Green122 Yellow66Orange139 Blue119Red87 TOTAL623

74. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 20 Questions Slide 20- 74 Part I Pages 469-470 Part II Pages 470 - 471 Part III Page 471 Part IV Page 472 24 1112 1418 2426

75. Chapter 20 Part I #2 Write the null and alternative hypotheses you would use to test each of the following situations. a) In the 1950s only about 40% of high school graduates went on to college. Has the percentage changed?

76. Chapter 20 Part I #2 Write the null and alternative hypotheses you would use to test each of the following situations. b) 20% of cars of a certain model have needed costly transmission work after being driven 50,000 and 100,000 miles. The manufacturer hopes that redesign of a transmission component has solved this problem.

77. Chapter 20 Part I #2 Write the null and alternative hypotheses you would use to test each of the following situations. c) We field test a new flavor soft drink, planning to market it only if we are sure that over 60% of the people like the flavor.

78. Chapter 20 Part I #2 Write the null and alternative hypotheses you would use to test each of the following situations. c) We field test a new flavor soft drink, planning to market it only if we are sure that over 60% of the people like the flavor.

79. Chapter 20 Part I #4 The seller of a loaded die claims that it will favor the outcome of 6. We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain. a) There’s a 3% chance that the die is fair. Incorrect

80. Chapter 20 Part I #4 The seller of a loaded die claims that it will favor the outcome of 6. We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain. b) There’s a 97% chance that the die is fair. Incorrect

81. Chapter 20 Part I #4 The seller of a loaded die claims that it will favor the outcome of 6. We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain. c) There’s a 3% chance that a loaded die could randomly produce the results we observed, so it’s reasonable to conclude that the die is fair. Incorrect

82. Chapter 20 Part I #4 The seller of a loaded die claims that it will favor the outcome of 6. We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain. d) There’s a 3% chance that a fair die could randomly produce the results we observed, so it’s reasonable to conclude that the die is loaded. Correct

83. Chapter 20 Part I #4 The seller of a loaded die claims that it will favor the outcome of 6. We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain. d) There’s a 3% chance that a fair die could randomly produce the results we observed, so it’s reasonable to conclude that the die is loaded. Correct

84. Chapter 20 Part I #11 11. In a rural area only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by “dowsing” – using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find that 27 have wells less than 100 feet deep. What do you conclude about his claim? (We consider a P-value of around 5% to represent strong evidence.)

85. Chapter 20 Part I #11 11. In a rural area only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by “dowsing” – using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find that 27 have wells less than 100 feet deep. What do you conclude about his claim? (We consider a P-value of around 5% to represent strong evidence.) a) Write appropriate hypotheses.

86. Chapter 20 Part I #11 11. In a rural area only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by “dowsing” – using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find that 27 have wells less than 100 feet deep. What do you conclude about his claim? (We consider a P-value of around 5% to represent strong evidence.) b) Check the necessary assumptions. Independence is reasonable for the customers checked, because the customers could be considered representative of all the dowser’s customers and 80 customers could be less than 10% of all of the dowser’s customers (if he has at least 800 customers). We would expect (80)(.30) = 24 successful wells and 56 wells that didn’t reach water within 100 feet. Both are at least 10, so the sample is reasonably large enough.

87. Chapter 20 Part I #11 11. In a rural area only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by “dowsing” – using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find that 27 have wells less than 100 feet deep. What do you conclude about his claim? (We consider a P-value of around 5% to represent strong evidence.) c) Perform the mechanics of the test. What is the P-value?

88. Chapter 20 Part I #11 11. In a rural area only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by “dowsing” – using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find that 27 have wells less than 100 feet deep. What do you conclude about his claim? (We consider a P-value of around 5% to represent strong evidence.) d) Explain carefully what the P-value means in this context.

89. Chapter 20 Part I #11 11. In a rural area only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by “dowsing” – using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find that 27 have wells less than 100 feet deep. What do you conclude about his claim? (We consider a P-value of around 5% to represent strong evidence.) e) What’s your conclusion? With a P-value of 0.231, we fail to reject the null hypothesis. There is insufficient evidence to suggest that the dowser has a success rate higher than 30%.

90. Chapter 20 Part I #11 11. In a rural area only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by “dowsing” – using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find that 27 have wells less than 100 feet deep. What do you conclude about his claim? (We consider a P-value of around 5% to represent strong evidence.) e) What’s your conclusion? With a P-value of 0.231, we fail to reject the null hypothesis. There is insufficient evidence to suggest that the dowser has a success rate higher than 30%.

91. Chapter 20 Part I #12 In the 1980s it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. (We consider a P-value of around 5% to represent strong evidence)

92. Chapter 20 Part I #12 In the 1980s it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. (We consider a P-value of around 5% to represent strong evidence) a) Write appropriate hypotheses.

93. Chapter 20 Part I #12 In the 1980s it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. (We consider a P-value of around 5% to represent strong evidence) b) Check the necessary assumptions. Independence is reasonable for the children studied, because the children studied could be considered representative of all children and 384 children is less than 10% of all children. We would expect (384)(.05) = 19.2 children with congenital abnormalities and 364.8 not to have abnormalities. Both are at least 10, so the sample is reasonably large enough.

94. Chapter 20 Part I #12 In the 1980s it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. (We consider a P-value of around 5% to represent strong evidence) c) Perform the mechanics of the test. What is the P-value?

95. Chapter 20 Part I #12 In the 1980s it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. (We consider a P-value of around 5% to represent strong evidence) d) Explain carefully what the P-value means in this context.

96. Chapter 20 Part I #12 In the 1980s it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. (We consider a P-value of around 5% to represent strong evidence) e) What’s your conclusion? With a P-value this low, we reject the null hypothesis. There is sufficient evidence that the current proportion of children with genetic abnormalities is greater than 5%.

97. Chapter 20 Part I #12 In the 1980s it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. (We consider a P-value of around 5% to represent strong evidence) f) Do environmental chemicals cause congenital abnormalities?

98. Chapter 20 Part I #12 In the 1980s it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. (We consider a P-value of around 5% to represent strong evidence) f) Do environmental chemicals cause congenital abnormalities?

99. Chapter 20 Part II #14 The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996 31% of students reported that their mother had graduated from college. In 2000, responses from 8368 students found that this figure had grown to 32%. Is this evidence of a change in education level among mothers?

100. Chapter 20 Part II #14 The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996 31% of students reported that their mother had graduated from college. In 2000, responses from 8368 students found that this figure had grown to 32%. Is this evidence of a change in education level among mothers? a) Write appropriate hypotheses.

101. Chapter 20 Part II #14 The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996 31% of students reported that their mother had graduated from college. In 2000, responses from 8368 students found that this figure had grown to 32%. Is this evidence of a change in education level among mothers? b) Check the assumptions and conditions. Independence is reasonable for the student’s surveyed, because the students surveyed could be considered representative of all students and 8368 students is less than 10% of all students. We would expect (8368)(.31) = 2594.08 student’s to have mothers with college degrees and 5773.92 not to have degrees. Both are at least 10, so the sample is reasonably large enough.

102. Chapter 20 Part II #14 The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996 31% of students reported that their mother had graduated from college. In 2000, responses from 8368 students found that this figure had grown to 32%. Is this evidence of a change in education level among mothers? c) Perform the test and find the P-value. z = -2 z = 2 P-value = 0.046 0.023

103. Chapter 20 Part II #14 The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996 31% of students reported that their mother had graduated from college. In 2000, responses from 8368 students found that this figure had grown to 32%. Is this evidence of a change in education level among mothers? d) State your conclusion.

104. Chapter 20 Part II #14 The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996 31% of students reported that their mother had graduated from college. In 2000, responses from 8368 students found that this figure had grown to 32%. Is this evidence of a change in education level among mothers? e) Do you think this difference is meaningful? Explain. More in chapter 21

105. Chapter 20 Part II #14 The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996 31% of students reported that their mother had graduated from college. In 2000, responses from 8368 students found that this figure had grown to 32%. Is this evidence of a change in education level among mothers? e) Do you think this difference is meaningful? Explain. More in chapter 21

106. Chapter 20 Part II #18 An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. The company goal is to keep the level of damaged machines below 2%. One day an inspector randomly checks 60 washers and finds that 5 of them have scratches or dents. Is this strong evidence that the warehouse is failing to meet the company goal? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

107. Chapter 20 Part II #18 An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. The company goal is to keep the level of damaged machines below 2%. One day an inspector randomly checks 60 washers and finds that 5 of them have scratches or dents. Is this strong evidence that the warehouse is failing to meet the company goal? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

108. Chapter 20 Part II #18 An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. The company goal is to keep the level of damaged machines below 2%. One day an inspector randomly checks 60 washers and finds that 5 of them have scratches or dents. Is this strong evidence that the warehouse is failing to meet the company goal? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

109. Chapter 20 Part II #24 Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty, and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain.

110. Chapter 20 Part II #24 Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty, and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain. Independence would be reasonable for the jurors, IF the people selected are representative of all potential jurors (Note: that is what we are determining) and 72 people is less than 10% of all potential jurors. We would expect (72)(.19) = 13.7 jurors to be Hispanic and 58.3 not to be. Both are at least 10, so the sample is reasonably large enough.

111. Chapter 20 Part II #24 Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty, and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain.

112. Chapter 20 Part II #24 Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty, and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain. Since the conditions are met, we can perform a one-proportion z-test.

113. Chapter 20 Part II #24 Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty, and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain.

114. Chapter 20 Part II #24 Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty, and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain. With a P-value this high, I fail to reject the null hypothesis. There is insufficient evidence to say that the proportion of Hispanics potential jurors is less than 19%. The jury selection system doe not appear to be unfair. The “apparent underrepresentation” here could be due to sampling variability.

115. Chapter 20 Part II #24 Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty, and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain. With a P-value this high, I fail to reject the null hypothesis.

116. Chapter 20 Part II #26 A study of the effects of acid rain on trees in the Hopkins Forest shows that of 100 trees sampled, 25 of them exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than the rest of the region? Comment, and write up your own conclusions based on an appropriate confidence interval as well as a hypothesis test. Include any assumptions you made about the data.

117. Chapter 20 Part II #26 A study of the effects of acid rain on trees in the Hopkins Forest shows that of 100 trees sampled, 25 of them exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than the rest of the region? Comment, and write up your own conclusions based on an appropriate confidence interval as well as a hypothesis test. Include any assumptions you made about the data.

118. Chapter 20 Part II #26 A study of the effects of acid rain on trees in the Hopkins Forest shows that of 100 trees sampled, 25 of them exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than the rest of the region? Comment, and write up your own conclusions based on an appropriate confidence interval as well as a hypothesis test. Include any assumptions you made about the data. Independence would be reasonable for the selected trees, because the trees sampled could be representative of all trees in Hopkins Forest and 100 trees is less than 10% of all trees in Hopkins Forest (as long as there are at least 1000 trees there). We would expect (100)(.15) = 15 trees with acid rain damage and 85 without damage. Both are at least 10, so the sample is reasonably large enough.

119. Chapter 20 Part II #26 A study of the effects of acid rain on trees in the Hopkins Forest shows that of 100 trees sampled, 25 of them exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than the rest of the region? Comment, and write up your own conclusions based on an appropriate confidence interval as well as a hypothesis test. Include any assumptions you made about the data. Since the conditions are met, we can perform a one-proportion z-test.

120. Chapter 20 Part II #26 A study of the effects of acid rain on trees in the Hopkins Forest shows that of 100 trees sampled, 25 of them exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than the rest of the region? Comment, and write up your own conclusions based on an appropriate confidence interval as well as a hypothesis test. Include any assumptions you made about the data.

121. Chapter 20 Part II #26 A study of the effects of acid rain on trees in the Hopkins Forest shows that of 100 trees sampled, 25 of them exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than the rest of the region? Comment, and write up your own conclusions based on an appropriate a hypothesis test. Include any assumptions you made about the data. With a P-value this low, I reject the null hypothesis. There is sufficient evidence to say that the proportion of trees damaged by acid rain in Hopkins Forest is higher than 15%.

122. Chapter 20 Part II #26 A study of the effects of acid rain on trees in the Hopkins Forest shows that of 100 trees sampled, 25 of them exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than the rest of the region? Comment, and write up your own conclusions based on an appropriate confidence interval as well as a hypothesis test. Include any assumptions you made about the data. With a P-value this low, I reject the null hypothesis. There is sufficient evidence to say that the proportion of trees damaged by acid rain in Hopkins Forest is higher than 15%. The trees in Hopkins forest appear to be more susceptible to acid rain than the rest of the Northeast region.