Question

multiple choice 4 points
select the most appropriate response.
3
in hypothesis testing, what is the function of a critical value that is obtained from the tables?
it is equal to the calculated statistic from the observed data.
it is the point on the number line where the decision changes from reject to fail to reject.
it is the center of the distribution of xs.
it is the point that is 1 standard deviation away from the mean.

Explanation:

Step1: Recall the definition of critical value

In hypothesis testing, the critical value is the point on the number line where the decision changes from reject to fail to reject.

Step2: Analyze other options

• The value equal to the calculated statistic from the observed data is the test - statistic, not the critical value.
• The center of the distribution of \(X\)'s is the mean (in case of symmetric distributions like normal), not the critical value.
• The point that is 1 standard deviation away from the mean is just a point in the distribution related to spread, not a decision - making point in hypothesis testing.

Answer:

It is the point on the number line where the decision changes from reject to fail to reject.