Henry performed a two- tailed test for an experiment in which N = 24. He could not find his table of t critical values, but he remembered the tcv at df = 13. He decided to compare his tobt with this tcv. Is he more likely to make a Type I or a Type II error in this situation?
To determine whether Henry is more likely to make a Type I or Type II error, we need to understand the concepts of Type I and Type II errors.
Type I error occurs when a null hypothesis is rejected when, in fact, it is true. This is also known as a false positive.
Type II error occurs when a null hypothesis is accepted when, in fact, it is false. This is also known as a false negative.
In Henry's situation, he performed a two-tailed test, which means he is testing for a difference in both directions. Generally, in hypothesis testing, we set a critical value (alpha level) to determine the threshold beyond which we reject the null hypothesis.
Since Henry couldn't find his table of t critical values but remembered the tcv at df = 13, we can assume that he will compare his t-value to this critical value. However, without knowing the specific t-value he obtained, we cannot definitively determine whether he will make a Type I or a Type II error.
Here's why:
If Henry's obtained t-value is less extreme (i.e., smaller) than the critical value at df = 13, then he might incorrectly accept the null hypothesis (Type II error) because his result is not significant enough to reject it.
On the other hand, if Henry's obtained t-value is more extreme (i.e., larger) than the critical value at df = 13, then he might incorrectly reject the null hypothesis (Type I error) because his result is significant even though it shouldn't be.
Therefore, without knowing the actual t-value obtained by Henry, it's impossible to determine conclusively whether he is more likely to make a Type I or Type II error in this situation.