Key for Practice Exam
          Exam 3 (Final), Spring 2001

1.  C           12. D
2.  B           13. D
3.  C           14. A
4.  D           15. B
5.  D           16. C
6.  D           17. D
7.  B           18. E (partial credit for B or C)
8.  B           19. D
9.  no answer   20. A
10. D           21. E (partial credit for C or D)
11. A           22. E


In the following solutions an underscore means to subscript and a
caret means to superscript.  For example, S^2 means S squared and
mu_{y|x} means mu sub y given x.

23.  mu_{y|x} = alpha + beta x = 98 + .95 x 51 = 146.45

     P(Y < 120) = P(Z < (120-146.45)/17) = P(Z < -1.56) = 0.0594

24.  P(Xbar > 6) = 1- P(Xbar < 6) = 1- P(Z < (6-5.6)/.4) = P(Z < 1) =
      0.1587

25.  a) Confounding variable: a variable that is related to the
     explanatory variable and to the response variable.

     b) Elevation is a confounding variable.  Response =
        presence/absence of houndstongue.  Explanatory variable =
        mountain goats.  Houndstongue is found at lower elevation.
        Mountain goats live at high elevations.

26.  n = (1.96 x sqrt{(.02)(.98)}/.01)^2 = 752.95.  use n = 753

27.  a) Positively skewed

     b) Yes, use lambda < 1

28.  a) leptokurtic (high kurtosis) or heavy tailed

     b) No

29.  Two assumptions are violated: linearity and constant variance.

30.  a) Early vs late crawling is independent of season of birth

     b) E = 224 x 97/425 = 51.125
            -----------------------------
     c)100  |      |      |      |      |
            |      |      |      |      |
            |   x  | x    |  x   |  x   |
            |      |      |      |      |
            |------|------|      |      |
        50  |      |      |      |      |
            |      |      |------|      |
            |      |      |      |------|
            |   y  |  y   |   y  |  y   |
            |      |      |      |      |
         0  |      |      |      |      |
            ----------------------------
              W      Sp     Su     F


            Key: x = late, y = early

    d) (2-1)(4-1) = 3

    e) Critical value = 7.81
       Reject Ho because 10.34 > 7.81

    f) Yes.  The X^2 test is significant revealing that crawling and
    season of birth are not independent.  The segmented bar graph
    shows that babies born in Summer or Fall are more likely to be
    late crawlers than babies born in Winter or Spring.