A statistical test is performed, and its P-value turns out to be about 3%. Which of the following must be true? Pick all that are correct.

The null hypothesis is true.

There is about a 3% chance that the null hypothesis is true.

The alternative hypothesis is true.

There is about a 97% chance that the alternative hypothesis is true.

If the null hypothesis were true, there would be about a 3% chance of getting data that were like those that were observed in the sample or even further in the direction of the alternative.

The P-value of about 3% was computed assuming that the null hypothesis was true

Thank you!!!

-If the null hypothesis were true, there would be about a 3% chance of getting data that were like those that were observed in the sample or even further in the direction of the alternative.

-The P-value of about 3% was computed assuming that the null hypothesis was true

To determine which options are correct, let's first understand what a p-value represents in the context of statistical testing.

The p-value is the probability of observing the data (or more extreme) if the null hypothesis is true. It measures the strength of evidence against the null hypothesis. A smaller p-value suggests stronger evidence against the null hypothesis.

Now, let's analyze each statement:

1. The null hypothesis is true.
- This statement is not necessarily true. The p-value only provides evidence against the null hypothesis but does not prove or disprove its truth.

2. There is about a 3% chance that the null hypothesis is true.
- This statement is incorrect. The p-value represents the probability of observing the data under the assumption that the null hypothesis is true, but it does not provide the chance or probability of the null hypothesis being true.

3. The alternative hypothesis is true.
- This statement is not necessarily true. The p-value alone does not directly indicate the truth of the alternative hypothesis.

4. There is about a 97% chance that the alternative hypothesis is true.
- This statement is incorrect. The p-value does not directly represent the chance or probability of the alternative hypothesis being true.

5. If the null hypothesis were true, there would be about a 3% chance of getting data that were like those that were observed in the sample or even further in the direction of the alternative.
- This statement is correct. The p-value represents the probability of observing data as extreme as those in the sample, or even more extreme, if the null hypothesis is true.

6. The p-value of about 3% was computed assuming that the null hypothesis was true.
- This statement is correct. The p-value is calculated under the assumption that the null hypothesis is true.

Correct statements: 5, 6.

Therefore, the correct statements are:
- There is about a 3% chance of getting data that were like those that were observed in the sample or even further in the direction of the alternative if the null hypothesis were true.
- The p-value of about 3% was computed assuming that the null hypothesis was true.