###In order to find p-values for Questions 1 and 2, use StatKey to create randomization distributions (one for each question, consisting of at least 5000 randomization samples each). Copy screenshots of both randomization distributions into your assignment. Its okay if you want to crop the screenshots you really just need randomization dot plots showing each p-value.

BEYOND THE NUMBERS 5.8 Computations versus Understanding Section Number: Name: to be praded, of assignments must be completed and submitted on the original book page Introduction It is important that you be able to compute correctly. However, computation prowess is no substitute for a deeper understanding of what you are doing and why. This is especially true in the field of statistical science. At the undergraduate level, computations are pretty easy. At all levels, however, the underlying concepts are challenging. The following activity will demonstrate and elucidate this divide. EXHIBIT 1 Eureka or Not? 3 Suppose that twenty identical experiments are taking place simultaneously around the world. The researchers are all studying the same drug, which they hope will improve the survival rate of the black- winged peckerwood finch after it has been infected with a particular type of tree mold. The survival rate left untreated is unfortunately only 32% None of the researchers know about the others' work. The table to the right shows the results from the 20 different studies. In all cases, the significance level was a = 0.05 and the hypothesis being TABLE 5.3 Finch Survival Rates Observed Site Survival Rate with Drug 1 0.35 2 0.34 0.31 4 0.33 5 0.33 6 0.35 7 0.35 8 0.33 9 0.30 10 0.34 11 0.34 12 0.30 13 0.34 14 0.31 15 0.31 16 0.31 17" 0.45 18 19 0.35 20 0.33 Number of Able to Reject Finches Studied Hip 0.32? 100 No n100 No 100 No n. 100 No n=100 No 100 NO n 100 No n 100 No n100 No n. 100 No n=100 No n. 100 No n = 100 No n=100 No n=100 No n100 No 100 Yes n100 No n=100 No n=100 No tested was 0.30 He: p=0.32 Hp > 0.32 Theme S: Hypothesis Testing 83 Questions 1. Use the data from Site 17 to confirm that the null could be rejected. What is the p-value associated with the result? Combine all of the studies (n = 100 20 = 2,000) and test the hypothesis again. Confirm that it cannot be rejected. Report the overall observed survival rate and the p-value associated with the overall test. 3. We have a dilemma. Nineteen of the sites don't seek publication because their results are not significant. Site 17 gets published because the results produced there, with an identical experiment, are significant. We know (though the researchers don't) that if we combine the results from all 20 sites, we will not be able to support the alternative. Describe what it means to have a Type 1 error rate of a = 0.05, and explain what has likely happened here in light of that definition 4. Do you think a ground-breaking scientific study should be replicated before it can be published? Why or why not? What steps should the scientific community take to improve study validity? 84 Theme 5: Hypothesis Testing BEYOND THE NUMBERS 5.8 Computations versus Understanding Section Number: Name: to be praded, of assignments must be completed and submitted on the original book page Introduction It is important that you be able to compute correctly. However, computation prowess is no substitute for a deeper understanding of what you are doing and why. This is especially true in the field of statistical science. At the undergraduate level, computations are pretty easy. At all levels, however, the underlying concepts are challenging. The following activity will demonstrate and elucidate this divide. EXHIBIT 1 Eureka or Not? 3 Suppose that twenty identical experiments are taking place simultaneously around the world. The researchers are all studying the same drug, which they hope will improve the survival rate of the black- winged peckerwood finch after it has been infected with a particular type of tree mold. The survival rate left untreated is unfortunately only 32% None of the researchers know about the others' work. The table to the right shows the results from the 20 different studies. In all cases, the significance level was a = 0.05 and the hypothesis being TABLE 5.3 Finch Survival Rates Observed Site Survival Rate with Drug 1 0.35 2 0.34 0.31 4 0.33 5 0.33 6 0.35 7 0.35 8 0.33 9 0.30 10 0.34 11 0.34 12 0.30 13 0.34 14 0.31 15 0.31 16 0.31 17" 0.45 18 19 0.35 20 0.33 Number of Able to Reject Finches Studied Hip 0.32? 100 No n100 No 100 No n. 100 No n=100 No 100 NO n 100 No n 100 No n100 No n. 100 No n=100 No n. 100 No n = 100 No n=100 No n=100 No n100 No 100 Yes n100 No n=100 No n=100 No tested was 0.30 He: p=0.32 Hp > 0.32 Theme S: Hypothesis Testing 83 Questions 1. Use the data from Site 17 to confirm that the null could be rejected. What is the p-value associated with the result? Combine all of the studies (n = 100 20 = 2,000) and test the hypothesis again. Confirm that it cannot be rejected. Report the overall observed survival rate and the p-value associated with the overall test. 3. We have a dilemma. Nineteen of the sites don't seek publication because their results are not significant. Site 17 gets published because the results produced there, with an identical experiment, are significant. We know (though the researchers don't) that if we combine the results from all 20 sites, we will not be able to support the alternative. Describe what it means to have a Type 1 error rate of a = 0.05, and explain what has likely happened here in light of that definition 4. Do you think a ground-breaking scientific study should be replicated before it can be published? Why or why not? What steps should the scientific community take to improve study validity? 84 Theme 5: Hypothesis Testing