Question

In statistical hypothesis testing, the area of non-rejection is defined as

• A. one minus probability of rejecting the Null hypothesis when it is true
• B. one minus probability of not rejecting the Null hypothesis when it is not true
• C. probability of rejecting the Null hypothesis when it is true minus probability of not rejecting the Null hypothesis when it is not true
• D. probability of rejecting the Null hypothesis when it is true

Hint:

In hypothesis testing, the non-rejection area corresponds to the probability of failing to reject the null hypothesis when it is false.

Answer 1

The Correct Option is A

Step 1: Understand the concept of non-rejection.
In statistical hypothesis testing, the term "non-rejection" refers to the probability that we fail to reject the null hypothesis when it is in fact true. This area corresponds to the acceptance region of the null hypothesis in the test. The concept of non-rejection is important in evaluating the power of a hypothesis test and understanding its behavior.
Step 2: Explanation of the options.
- Option (A) is correct. "One minus probability of rejecting the Null hypothesis when it is true" refers to the probability of correctly accepting the null hypothesis when it is true. This is the concept of "non-rejection."
- Option (B) is incorrect because it involves the probability of non-rejection when the null hypothesis is false, which isn't the definition of the non-rejection area.
- Option (C) is incorrect because it involves comparing the probabilities of rejection and non-rejection, which isn't a valid interpretation of the non-rejection area.
- Option (D) is incorrect because it refers only to rejection, not non-rejection.
Final Answer: \[ \boxed{\text{one minus probability of rejecting the Null hypothesis when it is true}} \]