Question

The following contingency table illustrates how a survey of public employees responded to questions regarding income and job satisfaction. Determine the probability of the following events and explain its meaning. (3 pts each) Table 14.14 Relationship between Income and job Satisfaction Iacome Job Satisfaction Low 100 60 40 Medium 30 80 40 10 Medium Hi 50 a. b. c. d. e. Medium job satisfaction At least medium income High job satisfaction or high income Lowjob satisfaction and medium income Low job satisfaction given low income

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Answer #1

Total sample size = 100 + 30 + 10 + 60 + 80 + 15 + 40 + 40 + 50 = 425

Hence,

a) P(Medium job satisfaction) = (60 + 80 + 15)/425 = 155/425 = 31/85 = 0.3647

b) P(Atleast medium income) = P(Medium) + P(High) = (30 + 80 + 40 + 10 + 15 + 50)/425 = 225/425 = 9/17 = 0.5294

c) P(High job satisfaction or high income) = (40 + 40 + 50 + 10 + 15)/425 = 155/425 = 31/85 = 0.3647

d) P(Low job satisfaction and medium income) = 30/425 = 6/85 = 0.0706

e) P(Low job satisfaction given low income) = 100/(100 + 60 + 40) = 100/200 = 1/2 = 0.50

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