X:  3.2  2.1  1.3  2.1  2.3  0.6  3.2  2.6  1.9  0.7
Y:  0.2  0.0  0.6  0.3  0.6  0.3  0.4  0.9  0.3  0.7

(1) Calculate sample means ,  and sample standard deviations sX, sY.
(2) Calculate sample covariance sXY and sample correlation rXY.

B. The random variable X is normally distributed around a mean of 10 with a variance of 36. The random variable Y is normally distributed around a mean of 5 with a variance of 16. The covariance of X and Y is known to be 12.

(1) Find Pr(-2<X<22) and Pr(4<X<16).
(2) Find X1 and X2 such that Pr(X>X1)=Pr(X<X2)=.025.
(3) Find ?XY, the correlation between X and Y.

C. Do Review Problems 5-20, 5-21, 5-22, and 5-23 in Wonnacott and Wonnacott, Introductory Statistics For Business and Economics, 4th ed.

D. Follow Example 3-9 in W&W (p. 90) and do a similar analysis with the 1984 Gallup survey data. Use V138 to construct a dichotomous variable for opinion about abortion (1,2,3=Favor; 5,6,7=Opposed; 4,8,9=Missing). Also construct variables for race and sex.

SYNTAX for abortion opinion: 
if ((v138 >= 1) and (v138 <= 3)) ABORTION=0 
if ((v138 >= 5) and (v138 <= 7)) ABORTION=1 
value labels ABORTION 0 'Favor' 1 'Oppose'

SYNTAX for race: 
compute RACE=0
if ((v039 = 1) or (v039 = 2)) RACE=1 
value labels RACE 0 'Nonwhite' 1 'White'

SYNTAX for sex:
compute SEX=0
if ((v039 = 1) or (v039 = 3) or (v039 = 5)) SEX=1
value labels SEX 0 'Female' 1 'Male'

(1) Use the SPSS command CROSSTABS to compute the sample joint distribution (i.e., crosstabulation) between ABORTION and RACE and between ABORTION and SEX. From the results, find the following probabilities and determine if ABORTION and RACE are statistically independent:

<a> Pr(ABORTION=0), Pr(ABORTION=0?RACE=0), and Pr(ABORTION=0?RACE=1)
<b> Pr(ABORTION=1), Pr(ABORTION=1?RACE=0), and Pr(ABORTION=1?RACE=1)

SYNTAX for crosstabs ABORTION by RACE:
crosstabs ABORTION by RACE SEX /cells=total

(2) From the results of the previous CROSSTABS command, find the following probabilities and determine if ABORTION and SEX are statistically independent:

<a> Pr(ABORTION=0), Pr(SEX=0), and Pr(ABORTION=0,SEX=0)
<b> Pr(ABORTION=0), Pr(SEX=1), and Pr(ABORTION=0,SEX=1)
<c> Pr(ABORTION=1), Pr(SEX=0), and Pr(ABORTION=1,SEX=0)
<d> Pr(ABORTION=1), Pr(SEX=0), and Pr(ABORTION=1,SEX=0)
 

E. Read Krehbiel, "Are Congressional Committees Composed of Preference Outliers?". Identify the two hypothesis tests (Test 1: HO1 vs. HA1 and Test 2: HO2 vs. HA2) in the following manner: 

(1) State the hypotheses for each test, using mathematical notations. (Note: Krehbiel made a notational mistake. Point out the mistake and correct it in your statement.)

(2) Interpret the substantive meaning of each test.

(3) Are the tests, as done by Krehbiel, one-tailed or two-tailed? Do you agree with Krehbiel's choice? If no, why?

(4) What are the statistics used for each test? What are their respective sampling distributions?