Test Bank - for Introduction to Econometrics 3rd Edition by H STOCK JAMES & W. WATSON MARK, All Chapters |Complete Guide A+

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, 4 Stock/Watson • Introduction to Econometrics, Third Edition


2.5. Let X denote temperature in F and Y denote temperature in C. Recall that Y = 0 when X = 32 and
Y =100 when X = 212; this implies Y = (100/180)  ( X − 32) or Y = −17.78 + (5/9)  X. Using Key
Concept 2.3, X = 70oF implies that  Y = −17.78 + (5/9)  70 = 21.11C, and X = 7oF implies
Y = (5/9)  7 = 3.89C.

2.6. The table shows that Pr ( X = 0, Y = 0) = 0037, Pr ( X = 0, Y = 1) = 0622,
Pr ( X = 1, Y = 0) = 0009, Pr ( X = 1, Y = 1) = 0332, Pr ( X = 0) = 0659, Pr ( X = 1) = 0341,
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Pr(Y = 0) = 0046, Pr (Y = 1) = 0954.
(a) E(Y ) = Y = 0  Pr(Y = 0) + 1 Pr (Y = 1)
= 0  0046 +1 0954 = 0954
#(unemployed)
(b) Unemployment Rate =
#(labor force)
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= Pr (Y = 0) = 1 − Pr(Y = 1) = 1 − E(Y ) = 1 − 0954 = 0.046
(c) Calculate the conditional probabilities first:
Pr ( X = 0, Y = 0) 0037
Pr (Y = 0| X = 0) = = = 0056,
Pr ( X = 0) 0659
Pr ( X = 0, Y = 1) 0622
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Pr (Y = 1| X = 0) = = = 0944,
Pr ( X = 0) 0659
Pr ( X = 1, Y = 0) 0009
Pr (Y = 0| X = 1) = = = 0026,
Pr ( X = 1) 0341
Pr ( X = 1, Y = 1) 0332
Pr (Y = 1| X = 1) = = = 0974
Pr ( X = 1) 0341
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The conditional expectations are
E(Y|X = 1) = 0  Pr (Y = 0| X = 1) +1 Pr (Y = 1| X = 1)
= 0  0026 + 1 0974 = 0974,
E(Y|X = 0) = 0  Pr (Y = 0| X = 0) + 1 Pr (Y = 1|X = 0)
= 0  0056 +1 0944 = 0944
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(d) Use the solution to part (b),
Unemployment rate for college graduates = 1 − E(Y|X = 1) = 1 − 0.974 = 0.026
Unemployment rate for non-college graduates = 1 − E(Y|X = 0) = 1 − 0.944 = 0.056
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(e) The probability that a randomly selected worker who is reported being unemployed is a
college graduate is
Pr ( X = 1, Y = 0) 0009
Pr ( X = 1|Y = 0) = = = 0196
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Pr (Y = 0) 0046

The probability that this worker is a non-college graduate is
Pr ( X = 0|Y = 0) = 1 − Pr ( X = 1|Y = 0) = 1 − 0196 = 0804




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