Question

SAT preparation A school counselor wants to compare the effectiveness of an online SAT preparation program with an in-person SAT preparation class. For an experiment, the counselor recruits $30$students who have already taken the SAT once. The response variable will be the improvement in SAT score.

a. Design an experiment that uses a completely randomized design to investigate this question.

b. Design an experiment that uses a matched pairs design to investigate this question. Explain your method of pairing.

c. Which design do you prefer? Explain your answer.

Short answer

(a) The experiment that uses a completely randomized design to investigate is assigning unique no. between one and thirty.

(b) The $15$corresponding students will receive the Online SAT preparation program first, followed by the in-person SAT preparation class whereas the remaining $15$students will receive the in-person SAT preparation class first, followed by the Online SAT preparation program.

(c) The design preferred is matched pairs experiment.

Step-by-step solution

Part (a) Step 1: Given information

We need to find the experiment that uses a completely randomized design to investigate.

Part (a) Step 2: Explanation

All subjects are randomly assigned to a group in a truly randomized experiment.

Let's give each of the $30$pupils a unique number between one and thirty (inclusive).

Draw $15$different numbers between one and thirty at random (including) using slips of paper, a random digits table, or technology.

The online SAT preparation program will be assigned to the fifteen students who correlate to the fifteen selected integers, while the in-person SAT preparation session will be assigned to the remaining fifteen students.

Part (b) step 2: Given information

We need to find an experiment that uses a matched pairs design to investigate.

Part (b) Step 2: Explanation

We know that

The fifteen corresponding students will receive the Online SAT preparation program first, followed by the in-person SAT preparation class (while taking the SATS between treatments), whereas the remaining fifteen students will receive the in-person SAT preparation class first, followed by the Online SAT preparation program (while the students take the SATS after each treatments).

Part (c) Step 1: Given information

We need to find the preferred design.

Part (c) Step 2: Explanation

We prefer the matched pairs experiment because there are more subjects assigned to each treatment than in a completely randomized experiment, and the two treatment groups are identical before the treatments begin, making it easier to compare treatment results and the differences in results more reliable (that is, we are more certain that the differences are due to the treatments).