Question at position 15 A track coach wants to test the effectiveness of a new training program for distance runners. He puts his fastest runners in a group and the slower runners in a group. He randomly assigns half of the fast runners to complete a new training program and the other half to complete the standard training. He does the same for the slower runners. He then compares race times for those who completed each training program separately within each group. This study uses which of the following experimental designs?Stratified random samplingSystematic random samplingA randomized block design, but not matched pairsA matched pairs designA completely randomized design

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The coach is organizing the runners into two distinct groups based on a pre-existing characteristic (speed: fast vs slow) before applying the experimental treatments, and then randomly assigning each runner within their speed group to either the new training program or the standard training. This approach uses blocking to control for a known source of variation (fast vs slow) and then randomizes within each block to compare treatments.

Option 1: Stratified random sampling. This is a sampling method used to select participants from a population, typically for observational studies or surveys, not an experimental design in which treatments are assigned and compared. It describes how subjects are chosen, not how treatments are allocated.

Option 2: Systematic random sampling. This is another sampling technique where every k-th individual is chosen from an ordered list; like stratified sampling, it pertains to sampling, not to how to assign experimental treatments within the study.

Option 3: A randomized block design, but not matched pairs. This option correctly characterizes the setup: the blocks are the speed groups (fast and slow), and within each block, runners are randomly assigned to the new or standard training. This design controls for block-level differences by randomizing within blocks, and it is distinct from matched-pairs because there is no direct pairing of individuals across treatments; instead, randomization occurs separately within each block.

Option 4: A matched pairs design. In a matched-pairs design, each subject receives both treatments or is paired with another subject so that comparisons are made within the pair. In this study, each runner experiences only one training program, and there are blocks by speed rather than direct pairs, so this option does not fit.

Option 5: A completely randomized design. Here, all runners would be randomized to treatments without considering the speed-based blocks. Since the design explicitly uses blocks to group runners by speed before randomization, it is not a completely randomized design.

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