A researcher wanted to find out if there was difference between older movie goers and younger movie goers with respect to their estimates of a successful actor€™s income. The researcher first identified Samuel L. Jackson as the top money maker based on data provided at www.boxofficemojo.com. Jackson€™s total gross earnings for 72 films was $5,016.9 million (an average of $69.7 million per film). The researcher then asked a random sample of older movie goers (50-60 years) and a random sample of younger movie goers (20-30 years) to give their best estimate of Samuel L. Jackson€™s average earnings per film. Carry out a nondirectional Mann-Whitney U Test on the estimates given by the two samples to find out if the distributions are equal. Follow the steps given below the table and use a significance level of .05.

Estimate of Samuel L. Jackson€™s
Average Earnings Per Film
(in millions)

Older Movie Goers ............................................ Younger Movie Goers
$40 ............................................................................. $80
$50 ........................................................................... $100
$200 ........................................................................... $90
$8 ............................................................................... $50
$2 ................................................................................. $1
$10 ............................................................................... $6
$12 ............................................................................. $15
$15 ............................................................................. $60
$20 ........................................................................... $300
$50 ............................................................................. $40

a. Present the null hypothesis.

b. Present the alternative hypothesis.

c. Identify the critical value of U by referring to Table E in your textbook.

d. Present the decision rule.
e. Calculate U.

f. Present a statistical decision.

g. Present a conclusion in the context of the research situation.

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Table E CRITICAL VALUES OF MANN-WHITNEY U FINDING p-VALUE If observed U is .larger than light number, p> .05 .between light and dark numbers, p <.05 .smaller than dark numbers, p<.01 NONDIRECTIONAL TEST .05 level of significance (light numbers) .01 level of significance (dark numbers) 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 3 4 13 13 10 11 11 12 2 11 12 13 14 15 17 10 18 11 19 12 20 13 10 11 13 14 16 17 10 11 20 22 13 15 19 21 12 13 24 26 16 18 22 15 28 19 24 16 30 21 25 17 27 18 34 24 10 12 14 16 18 10 12 32 22 10 13 15 17 19 13 22 24 15 17 23 26 28 18 20 26 18 29 20 31 22 34 36 26 42 31 38 28 45 33 41 30 48 36 11 24 2 10 12 17 15 20 11 13 31 22 34 24 37 27 39 29 16 11 14 17 20 13 23 26 29 16 18 21 26 30 33 37 18 21 24 33 36 24 39 42 29 31 45 34 48 37 52 39 58 45 55 42 62 48 11 26 13 16 19 10 16 23 13 40 27 47 36 11 44 51 39 55 42 30 33 11 14 18 12 22 26 29 18 21 33 24 37 41 31 45 34 49 37 53 41 57 44 61 47 65 51 69 54 15 27 13 12 16 10 13 20 24 28 33 17 37 41 31 45 50 34 38 45 50 55 34 38 42 59 45 63 49 67 53 72 56 76 60 54 42 20 24 14 13 17 11 22 15 26 31 18 22 36 26 40 30 59 46 64 50 67 54 74 58 78 83 63 67 15 39 44 49 33 29 37 47 53 36 41 54 59 42 46 59 64 45 50 64 10 14 19 12 24 29 16 20 26 31 18 22 27 34 24 70 55 75 60 80 64 85 90 51 69 73 96 79 16 11 15 21 13 37 42 31 70 75 60 81 65 86 70 92 74 55 11 17 22 10 15 12 18 24 11 16 34 28 39 19 24 29 30 36 42 21 26 31 99 105 93 75 81 99 106 112 81 87 45 51 34 39 48 55 37 42 57 63 67 49 54 75 81 60 65 87 70 86 44 18 61 47 67 53 74 58 80 64 86 70 93 75 92 19 13 19 12 25 17 32 38 22 28 41 34 24 30 45 33 48 36 52 58 65 72 78 39 45 51 56 62 55 69 42 48 54 85 69 90 92 74 99 106 81 87 113 119 93 99 119 127 99 105 63 20 13 20 13 27 18 76 83 60 67 98 105 112 86 92 73 79 |||| || ON7N 730 -|||||||||| |||| || || || || |||| || |||||I|||| |I 10 17 Table E" (Continued). CRITICAL VALUES OF MANN-WHITNEY U DIRECTIONAL TEST .05 level of significance (light numbers) .01 level of significance (dark numbers) 8 9 10 11 12 13 14 п 2 3 4 15 16 17 18 19 20 3 4 10 11 4 10 11 12 14 15 16 17 18 10 11 12 13 15 16 18 11 19 12 20 13 22 14 23 15 25 16 3 10 10 12 14 16 17 11 12 19 21 23 15 25 16 26 18 28 19 30 20 32 22 13 13 15 17 19 21 24 14 16 26 17 28 30 19 21 33 23 35 24 37 26 39 28 11 11 12 15 18 20 23 13 26 36 26 39 28 10 13 28 31 33 24 41 44 32 47 11 17 20 22 30 34 12 18 11 21 24 14 16 27 30 33 36 21 23 26 39 28 42 31 45 33 48 36 51 38 54 40 10 4 11 14 20 13 24 27 16 19 31 34 37 41 24 27 44 33 48 36 51 38 55 41 58 44 62 47 11 30 11 12 16 19 12 23 27 15 18 31 22 34 25 38 28 42 46 31 34 50 37 54 41 57 44 61 47 65 50 69 53 12 2 13 17 11 21 14 26 17 21 30 34 38 28 42 31 47 51 35 38 55 42 60 46 64 49 68 53 72 56 77 60 24 13 10 15 19 12 24 28 20 23 33 37 42 31 47 35 51 56 39 43 61 47 65 51 70 55 75 59 80 63 84 67 27 16 21 26 10 13 17 31 36 22 26 30 46 34 56 51 61 38 43 47 66 51 82 65 87 69 92 73 14 11 41 71 77 56 60 12 23 18 28 11 15 19 19 25 30 12 16 39 33 44 24 28 33 50 37 61 66 47 51 72 77 56 61 83 66 15 94 100 55 42 88 70 75 80 60 65 71 46 51 56 16 14 36 42 26 31 48 36 54 41 77 61 83 66 89 71 95 76 101 107 82 87 21 109 115 88 17 15 20 26 18 33 39 23 28 45 51 33 38 57 44 49 64 70 77 55 60 83 66 89 71 96 102 13 רך 82 93 18 16 22 28 14 19 35 24 41 48 30 36 55 41 61 47 68 53 75 82 59 65 88 70 95 102 109 82 116 123 94 100 123 130 101 76 88 19 10 17 23 30 15 20 37 26 44 51 32 38 58 44 65 50 72 56 80 87 63 69 84 92 100 107 67 73 94 101 75 109 82 116 88 94 107 20 4 11 18 25 32 16 39 47 54 62 69 53 77 60 115 123 93 100 130 138 107 114 10 22 28 34 40 47 80 87 |||| 2020 303 o30 || || ||