Can anyone explain the P-value in Hypothesis testing with example.....

CFA Level I
#1

[original post removed]

#2

Khan is pretty good at explanations:

https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/hypothesis-testing-and-p-values

#3

the p-value is the minimum level of significance that you would be able to reject the null hypothesis.

That means, if the p-value is .03, you could reject the null hypothesis for 90% confidence level (.10 level of significance), a 95% confidence level (.05 level of significance), allllll the way up to a 97% confidence level (.03 level of significance). With a p-value of .03, you could not reject the null at a 98% confidence because that would require a p-value of .02 or lower.

#4

Is it the rule applicable to both one-tail and two-tails testing ?

#5

Yes.

A p-value is nothing more nor less than an alpha: the alpha that puts your calculated t-value on the dividing line between acceptance and rejection.

#6

S2000magician :

Thank you for your response. I have another question :

Is it that each sample has its own P-value (i.e., different sample has different P-value) ?

#7

My pleasure.

If the test statistic is different (which it will likely be for different samples), the p-value will be different. Remember: the p-value is the level of significance that puts the calculated statistic on the brink of accept/reject; if that statistic is different, the p-value will be different.

#8

S2000 Magician can you please define what is joint probability? what is the simplest method to calculate it with an example. please i will be honoured.

#9

Joint probability is the probability of two (or more) things happeneng together. We write the probability of A and B happening together as P(AB).

For example: you see a car; what’s the probability that it’s a red Ferrari? That’s the joint probability that it’s a red car and that it’s a Ferrari.

For this exam, the easiest way to calculate it will be to use conditional probabilities: the probability of something happening given that something else has happened. We write the probability of A happening given that B has happened as P(A|B). The key formula is this:

P(AB) = P(A|B) × P(B).

Maybe one car in 100 (in your neighborhood) is a Ferrari, 20% of (all of) the cars are red, and 40% of Ferraris are red. Then the probability of seeing a red Ferrari is:

P(red Ferrari) = P(red|Ferrari) × P(Ferrari) = 0.40 × 0.01 = 0.004 = 0.4%

(Note: we don’t care that 20% of all cars are red; we didn’t need this fact in this problem.)