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8. A comparative study is performed; you are given the following information. The total number of subjects equals 33. The observed value of the test statistic is greater than 0. I used the website to obtain the exact P-value for Fisher's test for each of the three possible alternatives. These three P-values are below along with three bogus P-values.

Set 1: 0.2450 0.4688 0.9233 Set 2: 0.1445 0.2890 0.9625

(a) Which set contains the correct P-values: 1 or 2? (No explanation is needed.)

(b) For the set you selected in part (a), match each P-value to its alternative. (No explanation is needed.) Note: Even if you pick the wrong set in part (a), you can still get full credit for part (b)

9. A comparative study is performed; you are given the following information. The total number of subjects equals 29. The observed value of the test statistic is greater than 0. I used the website to obtain the exact P-value for Fisher's test for each of the three possible alternatives. These three P-values are below along with three bogus P-values. Set 1: 0.1445 0.2890 0.9622 Set 2: 0.0762 0.1297 0.9868

(a) Which set contains the correct P-values: 1 or 2? (No explanation is needed.)

(b) For the set you selected in part (a), match each P-value to its alternative. (No explanation is needed.) Note: Even if you pick the wrong set in part (a), you can still get full credit for part (b).

10. A comparative study yields the following numbers: n1 = 10, n2 = 20, m1 = 4 and m2 = 26. On the assumption the Skeptic is correct, list all possible values of the test statistic.

11. A balanced CRD is performed with a total of 600 subjects. There is a total of 237 successes, with 108 of the successes on the first treatment. Use the standard normal curve to obtain the approximate P-value for the third alternative, p1 6= p2

12. An unbalanced CRD is performed with a total of 800 subjects. Three hundred subjects are placed on the first treatment and 500 are placed on the second treatment. There is a total of 356 successes, with 126 of the successes on the first treatment. Use the standard normal curve to obtain the approximate P-value for the third alternative, p1 6= p2.

13. A sample space has three possible outcomes, B, C, and D. It is known that P(C) = P(D). The operation of the chance mechanism is simulated 10,000 times (runs). The sorted frequencies of the three outcomes (B, C, and D) are: 2322, 2360, and 5318. (a) What is your approximation of P(B)? To receive credit you must explain your answer. (b) What is the best approximation of P(C)? To receive credit you must explain your answer.

14. A sample space has four possible outcomes, A, B, C, and D. It is known that P(A) + P(B) = 0.60 and P(C) < P(D). The operation of the chance mechanism is simulated 10,000 times (runs). The sorted frequencies of the four outcomes (A, B, C, and D) are: 500, 1528, 2531, and 5441. Use these simulation results to approximate P(C) and P(D). To receive credit you must explain your answers.

15. On each of four days next week (Monday thru Thursday), Earl will shoot six free throws. Assume that Earl's shots satisfy the assumptions of Bernoulli trials with p = 0.37.

(a) Compute the probability that on any particular day Earl obtains exactly two successes. For future reference, if Earl obtains exactly two successes on any particular day, then we say that the event "Brad" has occurred.

(b) Refer to part (a). Compute the probability that: next week Brad will occur on Monday and Thursday and will not occur on Tuesday and Wednesday. (Note: You are being asked to compute one probability.)