Question

a new york times article titled for runners, soft ground can be hard on the body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. one position supported running on soft surfaces to relieve joints that were in recovery from injury. the second position supported running on hard surfaces since soft surfaces can be uneven, which may make worse those injuries a soft surface was intended to help. suppose we are given sufficient funds to run an experiment to study this topic. with no studies to support either position, which of the following hypotheses would be appropriate? the first position is more sensible, so this should be a one - sided test. in this case, we should form the alternative hypothesis around the second position. because we would be interested in any difference between running on hard and soft surfaces, we should use a two - sided hypothesis test. because there is uncertainty, we should postpone defining the hypotheses until after we collect data to guide the test. the second position makes the more sense, so this should be a one - sided test. in this case, we should form the alternative hypothesis around the first position. question help: post to forum

Explanation:

In hypothesis testing, when we are interested in any difference (not just a specific direction like one being better than the other) between two groups (here, running on hard and soft surfaces), a two - sided hypothesis test is appropriate. We have no prior evidence to suggest a particular direction of the effect (i.e., we don't know if soft is better for joint recovery or if hard is better despite unevenness of soft). Postponing hypothesis definition until after data collection is not valid as hypotheses should be set before data collection to avoid bias. Choosing a one - sided test because one position "seems" more sensible is not a valid statistical approach as it should be based on the research question (interest in any difference) rather than initial perception.

Answer:

Because we would be interested in any difference between running on hard and soft surfaces, we should use a two - sided hypothesis test.