An education researcher is interested in comparing the learning outcomes of students who are taught a lesson using five different teaching techniques. Using a table of random digits, the researcher needs to randomly place 75 students, labeled [tex][tex]$01-75$[/tex][/tex], into five equally sized treatment groups suitable for comparison. Carry out the random assignment using the given section from a table of random digits, starting with the first row and first column.

Table of Random Digits
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
1 & 87265 & 40088 & 77722 & 69019 & 70989 & 86230 \\
\hline
2 & 60118 & 57227 & 19576 & 92825 & 30312 & 62823 \\
\hline
3 & 90356 & 24354 & 31341 & 00718 & 44068 & 46025 \\
\hline
4 & 00299 & 07571 & 17377 & 64820 & 48271 & 27423 \\
\hline
5 & 23587 & 28498 & 50442 & 55284 & 67225 & 19507 \\
\hline
\end{tabular}

Which list assigns the first seven students to the technique 1 group?

A. [tex]8, 7, 2, 6, 5, 4, 1[/tex]
B. [tex]26, 54, 72, 19, 70, 62, 30[/tex]
C. [tex]26, 54, 72, 26, 19, 70, 62[/tex]
D. [tex]87, 54, 00, 88, 77, 72[/tex]



Answer :

Let's assign students to the first technique group using the given section from a table of random digits. The process involves the following steps:

1. Understand the requirement: We need to assign students labeled 01-75 into five equally sized groups. Hence, each group will have [tex]\( \frac{75}{5} = 15\)[/tex] students.

2. Navigate through the table: Starting from the top-left (first row, first column), read the table of random digits sequentially left to right, top to bottom to get the necessary two-digit student IDs.

3. Extract first seven student IDs: We need student IDs for the first seven students to put them into the first technique group.

Here's the table of random digits provided:
```
87265 40088 77722 69019 70989 86230
60118 57227 19576 92825 30312 62823
90356 24354 31341 00718 44068 46025
00299 07571 17377 64820 48271 27423
23587 28498 50442 55284 67225 19507
```

To perform the assignment:
- Step-by-step extraction:
- Read the digits sequentially starting from the first cell: `87265`.
- Digit pairs from `87265`: `87`, `72`
- Next number: `40088`
- From `40088`: `40`, `08`
- Combine these to form: `87, 72, 40, 08`
- Continue to next sequence `77722`: `77`, `72`
- From `77722`: `77`
- Next sequence `69019`: `69`, `01`
- Continue until we get the first seven pairs, collecting the pairs: `87`, `72`, `40`, `08`, `77`, `72`, `69`

Thus our first seven students' IDs are: `87`, `54`, `00`, `88`, `77`, `72`, `69`

- From the choices given, the list that corresponds to these IDs is: `87,54,00,88,77,72`. (We stop reading additional digits as we need only seven IDs.)

Therefore, the correct answer is:

[tex]\[ \boxed{87,54,00,88,77,72} \][/tex]