Random Variables and their PDFs

 Data Analysis Solutions

Solution 1: Students who live off campus are not drinking more than those who live on campus. A student’s drinking habits are independent of a student’s housing chioice.

Drink often Drink sometimes Never drink
Live off campus 50 .25 100 .51 47 .24 197
Live on campus 111 .25 221 .51 106 .24 438
161 .25 321 .50 153 .24 635

Drink often Drink sometimes Never drink
Live off campus 50 .31 100 .31 47 ..31 197 .31
Live on campus 111 ..69 221 .69 106 .69 438 .69
161 321 . 153 635

Solution 2: We can see that the proportions for parent involvement differ at each achievement level. Students success and parent participation are dependent.

Active parent participation Some parent participation No parent participation
Above grade level 8 .67 3 .25 1 .08 12
At grade level 13 .46 12 .43 3 .11 28
Below grade level 2 .10 12 .60 8 .40 20
23 .38 25 .42 12 .20 60

Solution 3: We see from our calculations that a voter’s party affiliation and position on Prop ZZ are independent.

Democrat Republic Other
Favor PropZZ 24 .33 18 .25 30 .42 72
Oppose 8 .33 6 .25 10 .42 24
32 33 24 .25 40 .42 96
Democrat Republic Other
Favor PropZZ 24 .75 18 ..75 30 .75 72 .75
Oppose 8 .25 6 .25 10 .25 24 .25
32 24 40 96