A school is implementing an SAT preparation program. To study the program’s effectiveness, the school looks at participants’ SAT scores before starting the program and after completing the program.

Question

Out of 100 students sampled, 80 increased their scores, 10 kept their scores the same, and 10 decreased their scores. How could this situation be simulated using a random digit table?

A) Assign the digit 0 to students who increased their scores, 1 to students whose scores remained the same, and 2 to students whose scores decreased. Use the random digit table to generate one-digit numbers, ignoring any values greater than 2.
B) Assign digits 0, 1, 2, 3, 4, 5, 6, and 7 to students who increased their scores. Assign 8 to students who kept their scores the same and 9 to students whose scores decreased. Use the random digit table to generate one-digit numbers.
C) Assign the number 80 to students who increased their scores, 10 to students whose scores remained the same, and 10 to students whose scores decreased. Use the random digit table to generate two-digit numbers, ignoring any values besides 80 and 10.
D) Assign digits 1, 2, 3, 4, 5, 6, 7, and 8 to students who decreased their scores. Assign 9 to students who kept their scores the same and 0 to students whose scores increased. Use the random digit table to generate one-digit numbers.

Answer 1

To simulate the situation of students' SAT score changes using a random digit table, we need to ensure that the assignments of digits correspond to the proportions of students in each category:

• 80 students increased their scores (80% of 100)
• 10 students kept their scores the same (10% of 100)
• 10 students decreased their scores (10% of 100)

Given this distribution, option A is a valid approach:

A) Assign the digit 0 to students who increased their scores, 1 to students whose scores remained the same, and 2 to students whose scores decreased. Use the random digit table to generate one-digit numbers, ignoring any values greater than 2.

This method works because:

• In the assignment:

  • 0 represents 80 students (increase),
  • 1 represents 10 students (no change),
  • 2 represents 10 students (decrease).

• The digits assigned correspond accurately to the proportions of each outcome, and by generating one-digit numbers and ignoring anything greater than 2, you ensure that the simulation reflects the actual scenario of the 100 students sampled.

In contrast, options B, C, and D do not correctly represent the proportions of students or include unnecessary digits, making A the only valid choice for simulation in this context.