Powel wants to find out how using fins increases swimming speed. This hypothesis could be tested with a counterbalanced repeated measures design by:
1. having half the swimmers swim without fins and the other half swim with fins.
2. having all swimmers first swim without fins and then swim with fins.
3. having half the swimmers first swim without fins and then with fins and having the other half swim first with fins and then without fins.
4. having all swimmers first swim with fins and then without fins.

having half the swimmers first swim without fins and then with fins and having the other half swim first with fins and then without fins.

Explanation:

counterbalanced repeated measures is methodology of experimentation in which sample for experiment is divided into two parts equally. The first follows the condition of experiment in one series of step while other part follows the steps precisely opposite to that of first part. The objective of such methodology is to cover each condition of experimentation and nullify any error condition for every sample. It also makes sure that in series of steps, sequence does not affect the result.

Since in the above experiment Powel wants to counterbalancing first he needs to divide the sample of swimmer into two parts. Then both parts should follows opposite steps.

This can be best followed by

in first half sample

second half sample

then compare the results of both set of sample.  It will make sure that both half corroborate the same result, also sequence of with and without fins does not effect the result and produce biased result.

based on this option 3 is correct answer.

is there multiple choice or do you need like an essay answer?