Which ONE of the following options describe correctly what does a probability value (or p value) from a hypothesis test tell us?

P value tells us how likely are the chance factors responsible for our observed results if null hypothesis was correct and there really was nothing going on in the population (i.e. no correlation or no association etc.)

P value tells us if null hypothesis is true.

P value tells us we can retain null when <.05 and reject null if .05 or higher. 

P value tells us to simply focus on the words 'Significant' and 'Not Significant' and not worry about the devil in the details.

P value tells us how likely are the chance factors responsible for our observed results if alternative hypothesis was correct with no correlation or no association etc.

P value tells us if null hypothesis is actually false.

The correct option is:

**P value tells us how likely are the chance factors responsible for our observed results if null hypothesis was correct and there really was nothing going on in the population (i.e. no correlation or no association etc.).**

This option accurately describes what a p-value represents. Specifically, the p-value helps us assess the probability of obtaining our observed results, or something more extreme, under the assumption that the null hypothesis is true. It does not directly tell us whether the null hypothesis is true or false but rather indicates how consistent the data are with the null hypothesis.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. What is the significance level (alpha) in hypothesis testing, and how is it related to the p-value?
2. How do you interpret a p-value of 0.03 in the context of a hypothesis test?
3. What are the potential limitations of relying solely on p-values in statistical analysis?
4. How does a p-value differ from a confidence interval in hypothesis testing?
5. Why is it important to understand the concept of statistical significance versus practical significance?

**Tip:** Always remember that a low p-value indicates that the observed data are unlikely under the null hypothesis, but it does not prove that the null hypothesis is false.

Explore the significance of p-values in hypothesis testing and their role in statistical analysis. Learn how p-values indicate the likelihood of chance factors affecting observed results under the null hypothesis. Suitable for advanced learners seeking a deeper understanding of statistical significance.

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