The *p*-value is the smallest level of significance at which the null hypothesis can be rejected. -> does this means we do not reject if t stat > p value?

How does this work?

The *p*-value is the smallest level of significance at which the null hypothesis can be rejected. -> does this means we do not reject if t stat > p value?

How does this work?

Fail to reject if the p-value is larger than the chosen significance level (alpha), such as 1% (0.01), 5% (0.05), etc. This corresponds to a critical t-value being larger than the calculated t-statistic.

Remember, p-values are probabilities, which cannot exeed 1 and cannot be less than 0. Calculated test statistics can be outside of this range.

A p-value is a level of significance.

An α is a level of significance.

You compare the p-value to the α you’ve chosen. Because the p-value is the _ **lowest** _ level of significance at which you’d *reject the null*, so *you reject the null at values of p or higher, but not at values lower than p*:

- If the chosen α > p, you reject the null
- If the chosen α < p, you don’t reject the null

Also, to help distinguish alpha and p-values-- a p-value is an **observed** significance level (based on the calculated test statistic) and an alpha is a **chosen** (or provided by CFAI) significance level that acts as a threshold (associated with a critical value).

Good clarification.

Thank you for the clarification guys

I am actually asking this question from CFAI - QM - Garfield Vignette Qns 5.

I still do not understand why is the answer fail to reject the null hypothesis.I cant seem to find alpha stated anywhere in the vignette…

Glad to help!

Did they mention a critical value for you to use as a cutoff, or do they state a p-value? I don’t have access to this info.

By convention, alpha values should be between 0.10 and 0.01 (10% and 1%, respectively). If they gave you a p-value larger than 0.10, they could assume that by general conventions the answer would involve a failure to reject the null.