Rescarchers are designing an experiment to compare two different types of running shoes, A and B, to investigate which type is better for minimizing running time for a one-mile run. The experiment will consist of distributing the shoes to runners who are classified as either professional or recreational. A randomized block 50 recreational runners w wear either the type A shoe or the type B shoe, and their running times will be recorded for a one-mile run.

(a) What is a statistical advantage of blocking by the classification of runner? design is planned, with blocking by classification of runner. Random samples of 50 professional runners and ill be selected. Each runner within each classification will be randomly assigned to

(b) Why is it important to randomize the type of shoe the runner will wear instead of allowing the runner to choose the shoe?

(c) Explain how the design of the experiment will address replication. What is the benefit of the replication?

A.) Blocking occurs in an experiment when a certain experimental unit is divided or split into groups based on a certain criteria. In the experiment above, the experiment was blocked for class of runner, either professional or recreational. This is essential in other to limit the possible variability in our experiment. It is very possible thatvtve response of each class of runner may differ, therefore, it good practice to block for class of runner in other to contain the variation.

B.) Randomizing the type of shoe being worn by the runner ensures that we have given each runner an equal chance of selecting any type of shoe available,thereby eliminating biases which might emanate from fixing shoe type for each runner.

C.) Replication could simply be defined as the application of a certain treatment on more than one experimental unit. In the experiment above, by blocking for class of runner, hence having the professional and recreational units, and treatment applied to each experimental unit, Hence giving the experimenter the chance of controlling variation in the experiment.

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