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.

FA25_QTM_100_3 Midterm Exam 2 - Requires Respondus LockDown Browser

View Explanation

Log in for full answers

Similar Questions

Question at position 14 A Type I error is committed when _________________.the validity of a claim was rejecteda true null hypothesis is rejectedthe critical value is greater than the value of the test statistica true alternative hypothesis is not acceptedClear my selection

What is the level of significance of a test?

The significance level in a hypothesis test corresponds to the maximum probability that

A two-sample t-test was conducted at the 𝛼 = 0.01 level of significance to determine if full scale IQ differs between children whose blood-lead levels <40 mg/100ml and children whose blood-lead levels > 40 mg/100ml. What is the probability of committing a Type I error?

What type of error might we have made? Explain what the error means in the context of the application.

More Practical Tools for International Students

Exam Browser Assistant

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler