Which of the following statements is/are true according to the logic of hypothesis testing?

Which of the following statements is/are true according to the logic of hypothesis testing?
1). When the null hypothesis is true, it should be rejected
2). When the null hypothesis is true, it should not be rejected
3). When the null hypothesis is false, it should be rejected
4). Both B and C are true

Which of the following statements is/are true according to the logic of hypothesis testing?

1). When the null hypothesis is true, it should be rejected

2). When the null hypothesis is true, it should not be rejected

3). When the null hypothesis is false, it should be rejected

4). Both B and C are true

Solution:

Hypothesis testing is a statistical method used to determine whether there is enough evidence to reject a null hypothesis ($H_0$). The decision is based on sample data and a predefined significance level ($\alpha$), usually 0.05 or 0.01.

Understanding the Statements:

1. When the null hypothesis is true, it should be rejected

- Incorrect. The null hypothesis should not be rejected if it is actually true. Rejecting $H_0$ when it is true is called a Type I error (false positive).

2. When the null hypothesis is true, it should not be rejected

- Correct. If $H_0$ is true, we should fail to reject it because there is no significant evidence against it.

3. When the null hypothesis is false, it should be rejected

- Correct. If $H_0$ is false, we should reject it in favor of the alternative hypothesis $H_1$. Failing to reject $H_0$ when it is false is a Type II error (false negative).

4. Both B and C are true

- Correct. Since statements B and C are both correct, option 4 is the right answer.

Conclusion:

The goal of hypothesis testing is to make the correct decision based on the available data. The ideal scenario is:
- Reject $H_0$ when it is false (correct decision).
- Fail to reject $H_0$ when it is true (correct decision).
- Avoid Type I and Type II errors as much as possible.

Thus, the correct answer is:
4). Both B and C are true.

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