Needing help to get this answer right.
_c___ 3. What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error?
a. As the alpha level increases, the size of the critical region increases and the risk of a Type I error increases.
b. As the alpha level increases, the size of the critical region increases and the risk of a Type I error decreases.
c. As the alpha level increases, the size of the critical region decreases and the risk of a Type I error increases.
d. As the alpha level increases, the size of the critical region decreases and the risk of a Type I error decreases.
Don't agree.
What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error?
The correct answer is d. As the alpha level increases, the size of the critical region decreases and the risk of a Type I error decreases.
To determine the correct answer to this question, you need to understand the relationship between the alpha level, the size of the critical region, and the risk of a Type I error.
The alpha level, also known as the significance level, is the probability of rejecting the null hypothesis when it is actually true. It is typically set before conducting a statistical test. The critical region is the range of test statistics that would lead to the rejection of the null hypothesis.
The risk of a Type I error refers to the probability of rejecting the null hypothesis when it is actually true. In simpler terms, it means falsely concluding that there is a significant effect or relationship when there isn't one.
Now let's analyze the options:
a. As the alpha level increases, the size of the critical region increases and the risk of a Type I error increases.
b. As the alpha level increases, the size of the critical region increases and the risk of a Type I error decreases.
c. As the alpha level increases, the size of the critical region decreases and the risk of a Type I error increases.
d. As the alpha level increases, the size of the critical region decreases and the risk of a Type I error decreases.
The correct answer is (a): As the alpha level increases, the size of the critical region increases and the risk of a Type I error increases.
Explanation:
When the alpha level is increased, it means that you are more lenient in rejecting the null hypothesis. This leads to a larger critical region, which includes a broader range of test statistics that would result in the rejection of the null hypothesis.
By widening the critical region, it becomes more likely for a test statistic to fall into that region and lead to the rejection of the null hypothesis, even if the null hypothesis is actually true. This increases the risk of a Type I error, which occurs when the null hypothesis is erroneously rejected.
In summary, increasing the alpha level increases the size of the critical region, making it more likely to reject the null hypothesis, and subsequently increases the risk of a Type I error.