Question 9 • Academy - Algebra, Functions, and Data Analysis
A researcher is comparing the effectiveness of three devices designed to help people who snore. There are 120 people who snore participating in the experiment. Using a table of random digits, the researcher will randomly place the participants into three equally sized treatment groups suitable for comparison.
Answer
A
Randomly number each person with 1, 2, or 3. Assign the people labeled 1 to the device 1 group, the people labeled 2 to the device 2 group, and the people labeled 3 to the device 3 group.
B
Number each participant from 1 to 120. Reading numbers from left to right from a random number table, identify 80 unique numbers from 1 to 120. Assign the people whose labels are the first 40 numbers to the device 1 group. Assign the people whose labels are the second 40 numbers to the device 2 group. Assign the remaining people to the device 3 group.
C
Number each participant from 000 to 119. Reading numbers from left to right on a random number table and looking at three digits at a time, identify 80 unique three-digit numbers from 000 to 119. Assign the people whose labels are the first 40 numbers to the device 1 group. Assign the people whose labels are the second 40 numbers to the device 2 group. Assign the remaining people to the device 3 group.
D
Select a participant, and identify the first digit reading numbers from left to right on a random number table. If the first digit is a 1, 2, or 3, assign the participant to the device 1 group. If the first digit is a 4, 5, or 6, assign the participant to the device 2 group. If the first digit is a 7, 8, or 9, assign the participant to the device 3 group. If the first digit is a 0, skip that digit and move to the next one to assign the participant to a group. Repeat this process for each participant.
Explanation
Number the 120 participants from 000 to 119, then read the random-digit table in three-digit groups and keep eligible numbers, skipping repeats and numbers above 119. The first 40 unique numbers selected form one group, the next 40 form another, and the 40 participants not selected form the third group. This guarantees three equally sized groups; choice D gives each person a chance at each device but does not guarantee equal group sizes.
AI-written and checked against the verified answer.