P-value of one-tailed test

CFA Level I Quant
#1

Could you please shed some clarifications on the following notes:

P-value is the probability of obtaining a critical value that would lead to the rejection of Ho.

For one-tailed test (upper tail) - where Ho is to be rejected when test stat is GREATER THAN the critical value - the p value is the probability that lies ABOVE the computed test stat.

Shouldn’t the p value be the prob that lies BELOW if the Ho is to be rejected? How is it possible that the prob that leads to the rejection of Ho is the one that lies above the test stat when Ho is rejected if test stat > critical value?

I’m confused over this. Please elaborate. Thanks

#2

A p-value is just an alpha; nothing more, nothing less. It’s the alpha that puts your calculated statistic on the border between acceptance and rejection.

If the p-value is less than the α you chose, then you reject the null hypothesis; this is the same conclusion you would reach if you compared your calculated statistic to the critical statistic.

If the p-value is greater than the α you chose, then you fail to reject the null hypothesis; this is the same conclusion you would reach if yo compared your calculated statistic to the critical statistic.