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

[michelin]

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?

 

[tickersu]

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.

 

[S2000magician]

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

 

[tickersu]

S2000magician wrote:
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).

 

[S2000magician]

tickersu wrote:

S2000magician wrote: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.

 

[michelin]

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….

 

[tickersu]

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.