Practice Exam Questions; Statistics 301; Professor Wardrop; Spring 2007Chapter 21. Sarah performs a CRD with a dichotomous re-sponse. She obtains the sampling distribution ofthe test statistic for Fisher’s test for her data; itis given below.x P (X = x) P (X ≤ x) P (X ≥ x)−0.6667 0.0001 0.0001 1.0000−0.5278 0.0024 0.0025 0.9999−0.3889 0.0242 0.0267 0.9975−0.2500 0.1104 0.1371 0.9733−0.1111 0.2588 0.3959 0.86290.0278 0.3220 0.7179 0.60410.1667 0.2094 0.9273 0.28210.3056 0.0652 0.9925 0.07270.4444 0.0075 1.0000 0.0075(a) Find the P-value for the first alternative(p1> p2) if x = 0.1667.(b) Find the P-value for the third alternative(p16= p2) if x = −0.2500.(c) Determine both the P-value and x that sat-isfy the following condition: The data arestatistically significant but not highly sta-tistically significant for the second alter-native (p1< p2).2. Sally performs a CRD with a dichotomous re-sponse. She obtains the sampling distributionof the test statistic for Fisher’s test for her data;it is given below.x P (X = x) P (X ≤ x) P (X ≥ x)−0.5000 0.0003 0.0003 1.0000−0.3920 0.0051 0.0054 0.9997−0.2841 0.0378 0.0432 0.9946−0.1761 0.1376 0.1808 0.9568−0.0682 0.2722 0.4530 0.81920.0398 0.3016 0.7546 0.54700.1477 0.1831 0.9377 0.24540.2557 0.0558 0.9935 0.06230.3636 0.0065 1.0000 0.0065(a) Find the P-value for the first alternative(p1> p2) if x = 0.1477.(b) Find the P-value for the third alternative(p16= p2) if x = −0.1761.(c) Determine both the P-value and x that sat-isfy the following condition: The data arestatistically significant but not highly sta-tistically significant for the second alter-native (p1< p2).3. Consider a balanced study with six subjects,identified as A, B, C, D, E and G. In the actualstudy,• Subjects A, B and C are assigned to thefirst treatment, and the other subjects areassigned to the second treatment.• There are exactly four successes, obtainedby A, D, E and G.This information is needed for parts (a)–(c) be-low.(a) Compute the observed value of the teststatistic.(b) Assume that the Skeptic is correct. Deter-mine the observed value of the test statis-tic for the assignment that places C, D andE on the first treatment, and the remainingsubjects on the second treatment.(c) We have obtained the sampling distribu-tion of the test statistic on the assumptionthat the Skeptic is correct. It also is possi-ble to obtain a sampling distribution of thetest statistic if the Skeptic is wrong pro-vided we specify exactly how the Skepticis in error. Assume that the Skeptic is cor-rect about subjects C, D and E, but incor-rect about subjects A, B and G.For the assignment that puts D, E and Gon the first treatment, and the other sub-jects on the second treatment, determinethe response for each of the six subjects.14. Consider an unbalanced study with six subjects,identified as A, B, C, D, E and G. In the actualstudy,• Subjects A and B are assigned to the firsttreatment, and the other subjects are as-signed to the second treatment.• There are exactly two successes, obtainedby A and C.This information is needed for parts (a)–(c) be-low.(a) Compute the observed value of the teststatistic.(b) Assume that the Skeptic is correct. Deter-mine the observed value of the test statis-tic for the assignment that places D and Eon the first treatment, and the remainingsubjects on the second treatment.(c) We have obtained the sampling distribu-tion of the test statistic on the assumptionthat the Skeptic is correct. It also is possi-ble to obtain a sampling distribution of thetest statistic if the Skeptic is wrong pro-vided we specify exactly how the Skepticis in error. Assume that the Skeptic is cor-rect about subjects A and G, but incorrectabout subjects B, C, D and E.For the assignment that puts D and G onthe first treatment, and the other subjectson the second treatment, determine the re-sponse for each of the six subjects.5. Two comparative studies are performed; you aregiven the following information.• The observed value of the test statistic isless than 0 in the first study and greaterthan 0 in the second study.• The first study is balanced.I used the website to obtain the exact P-valuefor Fisher’s test for each of the three possiblealternatives for each of the two studies, givingme a total of six P-values.My six P-values are: 0.0061, 0.0123, 0.3560,0.5572, 0.8346 and 0.9997.Match each P-value to its alternative and itsstudy.6. Two comparative studies are performed; you aregiven the following information.• The observed value of the test statistic isgreater than 0 in the both studies.• The second study is balanced.I used the website to obtain the exact P-valuefor Fisher’s test for each of the three possiblealternatives for each of the two studies, givingme a total of six P-values.My six P-values are: 0.0355, 0.0559, 0.3756,0.7512, 0.8297 and 0.9929.Match each P-value to its alternative and itsstudy.7. A comparative study yields the following num-bers: n1= 10, n2= 20, m1= 4 and m2= 26.On the assumption the Skeptic is correct, list allpossible values of the test statistic.8. A comparative study yields the following num-bers: n1= 20, n2= 10, m1= 6 and m2= 24.On the assumption the Skeptic is correct, list allpossible values of the test statistic.9. (Extra Credit Problem.) A balanced CRDwith n = 50 subjects is performed. The studyyields a total of 20 successes. Write an expres-sion for P (X = 0.00) using binomial coeffi-cients; do not compute the answer.10. (Extra Credit Problem.) A balanced CRDwith n = 40 subjects is performed. The studyyields a total of 14 successes. Write an expres-sion for P (X = 0.30) using binomial coeffi-cients; do not compute the answer.Chapter 311. A balanced CRD is performed with a total of600 subjects. There is a total of 237 successes,with 108 of the successes on the first treatment.2Use the standard normal curve to obtain theapproximate P-value for the third alternative,p16= p2.12. An unbalanced CRD is performed with a to-tal of 800 subjects. Three hundred subjects areplaced on the first treatment and 500 are placedon the second treatment. There is a total of 356successes, with 126 of the successes on the firsttreatment. Use the standard normal curve to ob-tain the approximate P-value for the third alter-native, p16= p2.13. A sample space has three possible outcomes, B,C, and D. It is known that P (C) = P (D). Theoperation of the chance mechanism is simulated10,000 times (runs). The sorted frequencies ofthe