A researcher wishes to find out whether giving a student 1 m

A researcher wishes to find out whether giving a student $1 million in cash will improve or ruin the student\'s grades in school. A high school class consists of the 8 students numbered in the following list. 0 Juanita 1 Tuan 2 Harry 3 Greta 4 William 5 Hiroshi 6 Betty 7 Jane Help the researcher by using the line from a table of random numbers (shown below) to assign 4 of these students to the treatment group. 39661 55832 02589 52612 25414 19879 60880 30641 55259 35324 Which students go in the treatment group? Tuan, Greta, Hiroshi, Betty Greta, nobody, Betty, Betty, Tuan, Hiroshi, Hiroshi Greta, nobody, Betty, Tuan, Hiroshi Greta, Harry, Hiroshi, William Hiroshi, Hiroshi, Harry, Hiroshi, nobody, Greta, Hiroshi, Greta, Harry, William

Solution

In the question, the population size is 8, while the treatment group size is 4. So the sample size is 8/4=2. Now pick a random number among 1 and 2; and mark that position in the random number table (line). Then we advance each time by 2 (the sample size), and mark those positions as well. If the list of random numbers is over, we wrap around and start marking the unmarked ones.

Choose a digit from the random numbers. We start with the 1st (say), and make lists of students corresponding to the digits:

Notice that the 10\'s choice produces the first 4 names in the option A.

You can experiment with the starting positions (instead of 1 or 2, start, say, at 5), and construct tables. Take the first 4 names from the list and make the sample.

(1)	1\'s	10\'s	100\'s	1000\'s	10000\'s
1)	1 (Tuan)	6 (Betty)	6 (Betty)	9 (Nobody)	3 (Greta)
2)	9 (Nobody)	8 (Nobody)	5 (Hiroshi)	2 (Harry)	0 (Juanita)
3)	4 (William)	1 (Tuan)	4 (William)	5 (Hiroshi)	2 (Harry)
4)	0 (Juanita)	8 (Nobody)	8 (Nobody)	0 (Juanita)	6 (Betty)
5)	9 (Nobody)	5 (Hiroshi)	2 (Harry)	5 (Hiroshi)	5 (Hiroshi)
6)	2 (Harry)	3 (Greta)	8 (Nobody)	5 (Hiroshi)	5 (Hiroshi)
7)	9 (Nobody)	7 (Jane)	8 (Nobody)	9 (Nobody)	1 (Tuan)
8)	4 (William)	2 (Harry)	3 (Greta)	5 (Hiroshi)	3 (Greta)
9)	1 (Tuan)	4 (William)	6 (Betty)	0 (Juanita)	3 (Greta)
10)	2 (Harry)	1 (Tuan)	6 (Betty)	2 (Harry)	5 (Hiroshi)