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InferenceScenarios_2013

Bossemploy ee level of satisfaction femalemale

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Boss/Employ ee Level of Satisfaction Female/Male Female/Female Male/Male Male/Female Overall Satisfied 23% 20% 47% 59% 38% Neutral 43% 40% 44% 32% 39% Dissatisfied 34% 39% 9% 9% 22% Total 100% 100% 100% 100% 100% Ranking 3 4 2 1 b) Carry out a hypothesis test to determine whether there sufficient evidence to infer that the level of job satisfaction depends on the boss/employee gender relationship. SOLUTION: Chi-square test of independence H 0 : Gender relationship and job satisfaction are independent. H a : Gender relationship and job satisfaction are dependent. OBSERVED Boss/Employ ee Level of Satisfaction Female/Male Female/Female Male/Male Male/Female Row Total Satisfied 21 25 54 71 171 Neutral 39 49 50 38 176 Dissatisfied 31 48 10 11 100 Column Total 91 122 114 120 447 EXPECTED Boss/Employ ee Level of Satisfaction Female/Mal e Female/Female Male/Male Male/Female Row Total Satisfied 34.8 46.7 43.6 45.9 171.0 Neutral 35.8 48.0 44.9 47.2 176.0 Dissatisfied 20.4 27.3 25.5 26.8 100.0 Column Total 91.0 122.0 114.0 120.0 447.0 9
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P-value = Pr(≥ 74.5) = virtually 0. Or: χ 2 * = = = 12.6 Both p-value < α and χ 2 > χ 2 * (extremely so!) so we strongly reject H 0 . The data provide strong evidence for statistically significant dependence between the qualitative variables, boss/employee gender relationship and job satisfaction. 10
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Scenario 10. Air Bags in Automobiles The following “ancient” data set from 1993 examines the presence of air bags in automobiles. Is there a relationship between the type of vehicle and what level of air bag implementation is standard equipment? AIR BAGS TYPE None Driver only Driver and passenger Total Small 16 5 0 21 Sporty 3 8 3 14 Compact 5 9 2 16 Midsize 4 11 7 22 Large 0 7 4 11 Van 6 3 0 9 Total 34 43 16 93 SOLUTION: Chi-square test of independence H o : Type of vehicle and airbag implementation are independent. H a : Type of vehicle and airbag implementation are dependent. For the 6x3 (full) table: Chi-square stat = 33.00 (10 df); P-value = .0003 Collapse categories as follows: Small+Sporty+Compact, Midsize+Large, Van Adding the cell counts gives the following: AIR BAGS TYPE None Driver only Driver and passenger Total Small/Sporty/ Compact 24 22 5 51 Midsize/Large 4 18 11 33 Van 6 3 0 9 Total 34 43 16 93 For this 3x3 full table: Chi-square stat = 18.24 (4 df); P-value = .0011 Combining Driver only + Driver and passenger gives the following: TYPE None Driver or Driver Total Small/Sporty/ Compact 24 27 51 Midsize/Large 4 29 33 Van 6 3 9 Total 34 59 93 For this 3x2 full table: Chi-square stat = 14.44 (2 df); P-value = .0007 Conclusion: There is a relationship between type of vehicle and airbag implementation. Larger cars are much more likely to have airbags; vans are different from larger cars, and are not likely to have airbags, especially on the passenger side. 11
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Scenario 11. Diet and Cholesterol A doctor investigating the effectiveness of different dietary advice in reducing blood cholesterol levels (mg/100ml) measured the levels before giving advice and again at the end of a six-month trial. A total of 19 subjects were randomly given certain dietary advice and their levels are shown below. Is there any difference in the relative effectiveness of the two types of advice given? Advice
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