Suppose in a survey of Americans’ education level and their happiness, the amoun
ID: 1189603 • Letter: S
Question
Suppose in a survey of Americans’ education level and their happiness, the amount of education was measured for each individual as following: X = 1 (elementary school completed, X=2 (high school completed), X=3 (college completed or more). Americans were asked to rank themselves on a “happiness index” as follows: H = 0 (not happy), H = 1 (fairly happy), or H = 2 (very happy). Then the joint probabilities of various
H
0
1
2
X
1
0.02
0.18
0.25
2
0.02
0.18
0.05
3
0.01
0.16
0.13
What is roughly the average education level in this survey?
What is the covariance and correlation?
Are education and happiness independent?
H
0
1
2
X
1
0.02
0.18
0.25
2
0.02
0.18
0.05
3
0.01
0.16
0.13
Explanation / Answer
P(X=1) = 0.02+0.18+0.25= 0.45
P(X=2) = 0.02+0.18+0.05= 0.25
P(X=3) = 0.30
Average level of education = 0.45*1 + 0.25*2 + 0.3*3 = 1.85
Yes education and happiness are correlated. We can see that the level of happiness varies with education level. This can be veried by a ANOVA matrix