A sports therapist was interested in evaluating whether stretching immediately before an event was better for sprinters than no stretching. She tested the null hypothesis that average sprinting times among athletes randomized to stretch before an event is equal to average sprinting times among athletes randomized to not stretch before an event. She found a p-value of 0.067. If she uses a 10% significance level instead of the usual 5% significance level, one consequence of this will be that:

Question

BlackTom AI · Accepted Answer

First, consider what a p-value of 0.067 means in the context of hypothesis testing. It represents the probability of observing data as extreme as or more extreme than what was observed if the null hypothesis is true. Now, examine the impact of changing the significance level (alpha) from 0.05 to 0.10.

Option 1: 'She is less likely to falsely conclude that stretching has a benefit if, in fact, it does not.' Increasing alpha makes it easier to reject H0, not harder. Thus, this statement is incorrect because raising alpha actually increases, not decreases, the chance of a Type I error when the null is true.

Option 2: 'She will definitely falsely conclude that stretching has a benefit if, in fact, it does not.' The word 'definitely' is too strong. While raising alpha increases the probability of a false positive, it does not guarantee one in every study. This option overstates the certainty and is therefore incorrect.

Option 3: 'She is more likely to falsely conclude that stretching has a benefit if, in fact, it does not.' This is the core idea: using a larger alpha (0.10) increases the likelihood of rejecting H0 when it is actually true, raising the Type I error rate compared to a 0.05 level. Since the p-value (0.067) is below 0.10 but above 0.05, the study would reject H0 at 0.10 but not at 0.05, illustrating the increased risk of a false positive with the higher threshold.

Option 4: 'none of them are correct.' Given the explanation above, at least option 3 captures the correct consequence, so this option is incorrect.

In summary, raising the significance level from 0.05 to 0.10 makes Type I errors more probable. Therefore, option 3 accurately describes the consequence in this scenario, while the other options misstate the relationship between alpha, p-values, and error types.

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