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6.78    A researcher looking for evidence of extrasensory perception (ESP) tests 500 subjects. Four of these subjects do significantly better (P <0.01) than random guessing.

(a)    Is it proper to conclude that these four people have ESP? Explain your answer.

(b)    What should the researcher now do to test whether any of these four subjects have ESP?

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6.79    One way to deal with the problem of misleading P-values when performing morę than one significance test is to adjust the criterion you use for statistical significance. The Bonferroni procedurę does this in a simple way. If you perform 2 tests and want to use the a & 5% significance level, you would reąuire a P-value of 0.05/2 = 0.025 to declare either one of the nuli hypotheses significant. In generał, if you perform k tests and want protection at level a, use a/k as your cutoff for statistical significance.

You perform 6 tests and calculate P-values of 0.476, 0.032, 0.241, 0.008, 0.010, 0.001. Which of these are statistically significant using the Bonferroni procedurę with a = 0.05?

6.80    Refer to the previous problem. A researcher has performed 12 tests of significance and wants to apply the Bonferroni procedurę with a = 0.05. The calculated P-values are 0.041, 0.569, 0.050, 0.416, 0.001, 0.004, 0.256, 0.041, 0.888, 0.010, 0.002, 0.433. Which of the nuli hypotheses are rejected with this procedurę?

6*81 The text cites an example in which researchers cairied out 77 separate

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