# The p-value is the smallest level of significance at which the null hypothesis can be rejected.

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…