alpha? p-value?

#1
Hi everyone,

I am very confused with p-value and alpha. I do appreciate your help.
Please take a look at the following questions and answers:

1) Accept Ho for alpha= 0.05. Then for alpha= 0.10, we...
ANS: We don't have enough information to perform any action because we don't know if p-value is >0.10 or < 0.10

2) Reject Ho for alpha = 0.05. Then for alpha = 0.10, we...
ANS: Reject Ho for alpha = 0.05 --> p-value < 0.05
--> p-value < 0.10 ---> Reject Ho for alpha = 0.10

I don't really understand why we have two alpha values to compare.
I thought we only have one alpha for the confidence interval.
And we perform our actions based on the rejection power(at certain Z scores)
as well as alpha...................
Please explain these answers to me....

Thank you very much.
 

JohnM

TS Contributor
#2
In hypothesis testing, we usually set it up with Ho, the null hypothesis, and Ha, the alternative hypothesis.

For example, the null (Ho) can be a statement about two or more means being equal. Ho: mu1=mu2

The alternative could be worded as the means not being equal.
Ha: mu1 not= mu2.
sometimes it looks like --> Ha: mu1 <> mu2

Now, we want to try to disprove Ho by collecting data to see if mu1 and mu2 are "different" enough to reject Ho. How different do they need to be? We determine that by setting an alpha level. If we want a lot of evidence that mu1 and mu2 are different before we reject Ho, we set alpha very low, say at .01. If we only want a little bit of evidence, maybe we would set it higher, around .10. Usually, in stats textbooks, the typical alpha level is set at .05.

Then when we do compare the data between mu1 and mu2, we will compute a test statistic, say a t-test (t statistic), and we determine how likely it would be to compute a t-statistic that large or larger, if in fact Ho is true. This likelihood, or probability, is the p-value.

If the p-value is less than or equal to the alpha level we set before collecting the data, then we have enough evidence to reject Ho. If the p-value is greater than alpha, then we don't have enough evidence to reject Ho (sometimes people say that we "accept" Ho, but that's not technically correct - we "fail to reject" Ho.)

For a more thorough explanation of hypothesis testing, go to this link and read through the sections:
http://davidmlane.com/hyperstat/logic_hypothesis.html
 
#3
Thanks for your help. =)
I understand that we have to compare Ho and H1 in order to make the decision; however, these two questions are still confusing to me. My question is, "Accept Ho for alpha= 0.05. Then for alpha= 0.10...," does alpha= 0.10 equal the p-value? Or does alpha = 0.10 equal the alpha of the confidence level?

Thanks again. :)
 

JohnM

TS Contributor
#4
Could you post the entire question, exactly as it's worded? That may help me understand what they're asking for.

Thanks.
 
#5
1) Suppose we Accept Ho for alpha = 0.05. Then for alpha = 0.10, we_____.
a) Accept Ho b) Reject Ho c) Not enough information
ANS: C
Accept Ho for alpha = 0.05 ---> p-value > 0.05.
However, we do not know if p-value > 0.10 or p-value < 0.10.
Therefore, NOT ENOUGH INFORMATION.

2) Suppose we Reject Ho for alpha = 0.05. Then for alpha= 0.10, we_____.
a) Accept Ho b) Reject Ho c) Not enough information
ANS: B
Reject Ho for alpha = 0.05 ---> p-value < 0.05.
p-value < 0.10 ---> Reject Ho for alpha = 0.10

3) Suppose we Accept Ho for alpha = 0.05. Then for alpha = 0.01, we_____.
a) Accept Ho b) Reject Ho c) Not enough information
ANS: A
Accept Ho for alpha = 0.05 --> p-value > 0.05.
---> p-value > 0.01 --> Accept Ho for alpha = 0.01.

4) Suppose we Reject Ho for alpha = 0.05. Then for alpha = 0.01, we_____.
a) Accept Ho b) Reject Ho c) Not enough information
ANS: C
Reject Ho for alpha = 0.05 --> p-value < 0.05.
However, we do not know if p-value > 0.01 or p-value < 0.01.
NOT ENOUGH INFORMATION

Thank you very much!! :tup:
 

JohnM

TS Contributor
#6
alpha, which is set prior to collecting data, is compared to the p-value. If the p-value is less than or equal to alpha, we reject Ho, otherwise, we "accept" Ho.

What these questions are trying to do is see if you understand how a different alpha may / may not affect the decision to accept / reject Ho.
 

BGM

TS Contributor
#8
alpha, which is set prior to collecting data,
Usually that it is chosen by the user a priori and theoretically it can be quite arbitrary. In practice many people choose 5% as a rule of thumb, but it really depends on your purpose - how "conservative" you want to be.

BTW you can always start a new thread in stead of pushing old thread, although your topics are similar.