STATISTICS . help please
Chapters 5-7 . Alex had successes on his first and last tri- als; Bruce had a success on his first trial 15. On each of four days next week (Monday thru and a failure on his last trial. Thursday), Earl will shoot six free throws. As- sume that Earl's shots satisfy the assumptions . Alex performed better after a failure than of Bernoulli trials with p = 0.37. after a success; and Bruce performed bet- ter after a success than after a failure. (a) Compute the probability that on any par- ticular day Earl obtains exactly two suc- cesses. For future reference, if Earl ob- For each man, identify his two tables from the tains exactly two successes on any partic- tables below, Hint: For each man, choose one ular day, then we say that the event "Brad" from Tables 1-3 and one from Tables 4-11. has occurred. (Hint: If there is more than one table that sat- (b) Refer to part (a). Compute the probability islies the conditions stated above, just give me one of them.) that: next week Brad will occur on Mon- day and Thursday and will not occur on Tuesday and Wednesday. (Note: You are being asked to compute one probability.) Table 1 Table 2 16. On each of four days next week (Monday thru Half F Total | Half S Total 35 65 100 Ist 45 35 TO0 Thursday), Dan will shoot five free throws. As- 2nd 55 45 100 2nd 45 55 100 sume that Dan's shots satisfy the assumptions Total 90 110 200 Total 90 110 200 of Bernoulli trials with p = 0.74. Table 3 (a) Compute the probability that on any par- Half F Total ticular day Dan obtains exactly three suc- 70 30 100 cesses. For future reference, if Dan ob- 2nd 20 80 100 tains exactly three successes on any partic- Total 90 110 200 ular day, then we say that the event "Mel" has occurred. (b) Refer to part (a). Compute the probabil- ity that; next week Mel will occur exactly Table 4 Table 5 once and that one occurrence will be on Current Current Prev. S F Total | Prev. S Monday, (Note: You are being asked to F Total S 43 46 30 59 compute one probability.) 46 64 110 59 110 Total 89 110 199 Total 89 110 17. Alex and Bruce each perform 200 dichotomous trials. A success is the desirable outcome; it re- Table 6 Table 7 quires more skill than does a failure. You are Current Current given the following information. Prev. S F Total | Prev. S Total 43 47 90 S 3.3 57 90 . Each of the men achieves exactly 90 suc- F 47 62 109 57 52 109 ceases. Total 109 199 Total 90 109 . Alex exhibited evidence of improving skill over time; and Bruce exhibited evi- dence of declining skill over time.Table 8 Table 9 Current Current Table 4 Table 5 Prev. S F Total Prev. S F Total Current Current S 46 43 89 36 53 89 Prev S F Total Prev. S F Total F 44 66 110 54 56 110 47 42 89 S 52 37 89 Total 90 109 199 Total 90 109 190 42 28 70 37 70 Total 89 70 159 Total Table 10 Table I1 Current Current Table 6 Prev S F Total Prev. Total 6 / 22 Current S 45 45 90 35 35 90 Prev. S F Total Prev. F 44 65 109 54 55 109 S 54 36 90 F F 48 42 90 Total 89 110 199 Total 89 110 199 36 33 69 42 27 69 Total 90 69 159 Total 90 69 159 18. Abby and Dana each perform 160 dichotomous trials. A success is the desirable outcome; it re- quires more skill than does a failure. You are Table 8 Table 9 given the following information. Current Current Prev. S F Total |Prev. S F Total . Each of the women achieves exactly 90 53 36 89 S 47 42 successes. 37 33 70 F 89 43 27 70 Total 90 69 159 Total 69 159 . Abby exhibited evidence of improving skill over time; and Dana exhibited no ev- Table 10 Table 11 idence of changing skill over time. Current Current . Abby had failures on her first and last tri- Prev. SF Total | Prev. SF Total als; Dana had a failure on her first trial and 48 42 F 90 53 37 90 a success on her last trial. 41 28 F 36 33 69 Total 89 70 159 Total 89 70 159 . Abby performed better after a success than after a failure; and Dana performed better after a failure than after a success. 19. A box contains 14 red cards and six blue cards For each woman, identify her two tables from for a total of 20 cards. Walt is going to select the tables below. Hint: For each woman, choose n = 10 cards at random with replacement from one from Tables 1-3 and one from Tables 4-1 1. the box. Let W denote the number of red cards (Hint: If there is more than one table that sat- that Walt obtains. Let X denote the number of isfies the conditions stated above, just give me blue cards that Walt obtains. Yale is going to one of them. If no table satisfies the conditions, select n = 10 cards at random without replace- say it is impossible.) ment from the box. Let Y denote the number of red cards that Yale obtains. Finally, let Z de- Table 1 Table 2 note the number of blue cards that Yale obtains. Half S F Total | Half S F Total You may use the fact that the probability his- Ist 35 45 Ist 50 30 80 $5 25 80 2nd 40 tograms of the sampling distributions of W. X, 2nd 40 80 Total 90 70 70 160 Y' and Z are pictured below. The number above 160 Total each rectangle is its height which also equals Table 3 its area. Note that O means zero, whereas .000 Half S F Total means smaller than .0005, but not zero. Ist 45 35 2nd 45 35 80 (a) Place an X next to the probability his- Total 90 70 160 togram of the sampling distribution of X
