Homework #3 (due Oct 20)

In 1970, the U.S. had a draft lottery to help select males between the ages of 19 and 26 for induction into the armed forces. The system was supposed to create a "random" ordering of the 366 days of the year (including February 29). Each day of the year was typed on a slip of paper and inserted into a capsule. The capsules were mixed and assigned a "drawing number" according to their position in the sequence of capsules picked from a bowl. The table summarizes the results. The dates are grouped by month, and the drawing numbers by thirds.

Drawn Numbers	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec	Total
1-122	9	7	5	8	9	11	12	13	10	9	12	17	122
123-244	12	12	10	8	7	7	7	7	15	15	12	10	122
245-366	10	10	16	14	15	12	12	11	5	7	6	4	122
Totals	31	29	31	30	31	30	31	31	30	31	30	31	366

Is there evidence in the table to cast suspicion on the randomness of the sequence of drawing numbers?

In 1963, the President’s Task Force on Manpower Conservation interviewed a national sample of 2400 young males rejected for military service because of failure to pass the Armed Forces Qualification Test. The following data set contains data for 2294 armed forces rejectees cross-classified by their education (grammar school, some high school, high school graduate, their father’s education (grammar school, some high school, high school graduate, not available [NA}), age (less than 22, 22 or older), and race (white, black). We’ll take the rejectee’s education as the dependent variable in the analysis. Find a parsimonious fit to the data. Do you think the missing values are "missing at random"?

In the data, the education categories for variables SonED & DadEd are

1 = grammar school,

2 = some high school

3 = high school graduate

4 = missing

The variable GE22 is 1 if the respondent’s age is 22 or more, 0 otherwise.

The variable White is 1 if the respondent is white and 0 if he is African-American.

Count SonEd DadEd GE22 White

39 1 1 0 1

4 1 2 0 1

11 1 3 0 1

48 1 4 0 1

29 2 1 0 1

8 2 2 0 1

9 2 3 0 1

17 2 4 0 1

8 3 1 0 1

1 3 2 0 1

6 3 3 0 1

8 3 4 0 1

231 1 1 1 1

17 1 2 1 1

18 1 3 1 1

197 1 4 1 1

115 2 1 1 1

21 2 2 1 1

28 2 3 1 1

111 2 4 1 1

51 3 1 1 1

13 3 2 1 1

45 3 3 1 1

35 3 4 1 1

19 1 1 0 0

5 1 2 0 0

2 1 3 0 0

49 1 4 0 0

40 2 1 0 0

17 2 2 0 0

14 2 3 0 0

79 2 4 0 0

19 3 1 0 0

7 3 2 0 0

3 3 3 0 0

24 3 4 0 0

110 1 1 1 0

18 1 2 1 0

11 1 3 1 0

178 1 4 1 0

133 2 1 1 0

38 2 2 1 0

25 2 3 1 0

206 2 4 1 0

103 3 1 1 0

25 3 2 1 0

18 3 3 1 0

81 3 4 1 0