Question

In: Statistics and Probability

do males or female feel more tense or stress out at work?A survey of employed adults...

do males or female feel more tense or stress out at work?A survey of employed adults conducted online revealed the following. in the space below, draw a decision tree diagram and answer the question a-d. your answer should be demonstrably derived via decision tree.
a.   Given that the employed adults felt tense or stress out at work, what is the probability that the employed adults was a male
b.   Given that the employed adults is a male, what is the probability that he felt tense or stress out at work
c.   is the feeling tense or stress out at work and gender independent
                             Yes.                No.               Sum
male.                   244.              495.               739
Female.              282.              480.                762
Sum.                   526.              975.                1501

Solutions

Expert Solution

a.   Given that the employed adults felt tense or stress out at work, what is the probability that the employed adults was a male

required probability=P(male|tense)=P(male and tense)/P(tense)=(244/1501)/(526/1501)=244/526=0.4639
b.   Given that the employed adults is a male, what is the probability that he felt tense or stress out at work

required probability=P(tense|male)=P(male and tense)/P(male)=(244/1501)/(739/1501)=244/739=0.3302
c.   is the feeling tense or stress out at work and gender independent

here we use chi-square test with

null hypothesis H0: feeling tense or stress out at work and gender are independent

alternate hypothesis Ha: feeling tense or stress out at work and gender are not independent

chi-square=sum((O-E)2/E)=2.62 with (r-1)(c-1)=(2-1)(2-1)=1 df

critical chi-square(0.05,1)=3.84 is more than calculated chi-square , so we fail to reject(or accept) null hypothesis and conclude that feeling tense or stress out at work and gender independent

observed(O) Expected(E) E (O-E) (O-E)2/E
244 526*739/1501 258.97 -14.97 0.87
495 975*739/1501 480.03 14.97 0.47
282 526*762/1501 267.03 14.97 0.84
480 975*762/1501 494.97 -14.97 0.45
sum= 1501 0 1501 0 2.62

orchestra answered 1 year ago
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