Question

question 4 (10 points)
a university financial aid office wants to estimate how much students earn from summer employment to help determine financial aid levels. the population consists of 975 students who have completed at least one year of study but have not yet graduated. a random sample of 50 students will be selected from an alphabetized list and sent a questionnaire.
a. explain clearly how you would use a random digits table to select a simple random sample of 50 students from this population.
b. beginning at the top line in the random digits table below, show the first 8 students that are selected using the method described in part a). mark on the table or write below the table to show your method clearly.
11164 36318 75061 37674
21215 91791 76831 58678
10438 44482 66558 37649
36792 26236 33266 66583
c. the university will repeat the survey the following year but will use a stratified random sample instead. suggest a variable to stratify by and justify your choice.

Explanation:

a. Explanation:

Step1: Assign numbers

Assign each of the 975 students a unique 3 - digit number from 001 to 975.

Step2: Select digits

Use the random digits table. Read 3 - digit numbers from the table. If the 3 - digit number is between 001 and 975, select the corresponding student. If the number is 000 or greater than 975, skip it. Repeat this process until 50 unique students are selected.

b. Explanation:

Step1: Read first 3 - digit numbers

Starting at the top line:

• 111: Select student 111
• 643: Select student 643 (but wait, we need to check if it's in range. Since we have 975 students (001 - 975), 643 is valid.
• 631: Select student 631
• 875: Skip (875>975)
• 061: Select student 061
• 376: Select student 376
• 742: Skip (742 is not relevant as we take 3 - digit numbers. Wait, actually, we should group the digits into 3 - digit numbers. The first line is 11164 36318 75061 37674. Grouping as 111, 643 (invalid as 643 is not in 001 - 975? No, wait 643 is within 001 - 975. Then 363, 187 (skip 187>975), 506, 137 (skip 137 is not in 001 - 975? No, 137 is valid. Wait, no, the correct way:

Take the first line: 11164 36318 75061 37674.
Group as 111 (valid), 643 (valid), 631 (valid), 875 (invalid), 061 (valid), 376 (valid), 742 (invalid).
Second line: 21215 91791 76831 58678. Group as 212 (valid), 159 (valid), 179 (valid), 176 (valid), 831 (valid), 586 (valid), 78 (invalid (needs 3 - digit, so 078? If we assume leading zeros. Wait, no, the students are numbered 001 - 975. So if we get a two - digit number like 78, we can write it as 078.
First 8 students: 111, 061, 212, 159, 179, 176, 078, 363

c. Explanation:

Step1: Suggest a variable

A variable to stratify by could be the class level (freshman, sophomore, junior).

Step2: Justify

Students in different class levels may have different earning potentials from summer employment. For example, juniors may have more work experience and thus earn more than freshmen. Stratifying by class level will ensure that each class level is represented proportionally in the sample and will reduce the variability within each stratum, leading to a more accurate estimate of the population mean summer earnings.

Answer:

a. Assign 3 - digit numbers 001 - 975. Read 3 - digit from table, select if in range.
b. 111, 061, 212, 159, 179, 176, 078, 363
c. Class level. Different class levels may have different earnings. Stratifying reduces variability.