Kitten261002
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Hi,

This has been bothering me for a while, so I thought I'd get some help from the TSR community, as my teacher can't seem to answer it.

Could somebody please try answering this as thoroughly as possible?

Why do we reject the null hypothesis when the p value is less than the significance level?

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For example, in the question above, why is the null hypothesis rejected when P (x<= 0.08)<0.05 ?

I thought that we'd reject the null hypothesis when P (x<= 0.08)>0.05 ?

Thank you in advance for all the help!
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RDKGames
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(Original post by Kitten261002)
Hi,

This has been bothering me for a while, so I thought I'd get some help from the TSR community, as my teacher can't seem to answer it.

Could somebody please try answering this as thoroughly as possible?

Why do we reject the null hypothesis when the p value is less than the significance level?

For example, in the question above, why is the null hypothesis rejected when P (x<= 0.08)<0.05 ?

I thought that we'd reject the null hypothesis when P (x<= 0.08)>0.05 ?

Thank you in advance for all the help!
In every hypothesis test you have your null hypothesis H_0 which is the boring statement about what you have observed over long periods of time. It becomes your go-to statement.

You also have the more exciting alternate hypothesis H_1 which aims to challenge H_0, but before we sway to reject H_0 in favour of H_1, we need to mathematically establish when it is acceptable to do so.

If you observe an event taking place in a particular sample, then you need to see what the likelihood of this event occuring is if you assume H_0 to be true.

Now the kicker is that if the probability of this event happening is VERY small, i.e. below a certain treshold which we denote as the level of significance, then it should make you think that it is extremely unlikely that this event has occured purely due to luck, and thus it is a statistically significant result because it suggests a shift away from the null hypothesis.

If this turns out to be true, i.e. p value is less than sig level, then you reject the null hypothesis as it is not longer a suitable statement. You do not accept the alternate hypothesis however either as you need to be careful.

P.S. This might help you understand a bit more: https://opentextbc.ca/researchmethod...hesis-testing/
Last edited by RDKGames; 2 months ago
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Kitten261002
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(Original post by RDKGames)
In every hypothesis test you have your null hypothesis H_0 which is the boring statement about what you have observed over long periods of time. It becomes your go-to statement.

You also have the more exciting alternate hypothesis H_1 which aims to challenge H_0, but before we sway to reject H_0 in favour of H_1, we need to mathematically establish when it is acceptable to do so.

If you observe an event taking place in a particular sample, then you need to see what the likelihood of this event occuring is if you assume H_0 to be true.

Now the kicker is that if the probability of this event happening is VERY small, i.e. below a certain treshold which we denote as the level of significance, then it should make you think that it is extremely unlikely that this event has occured purely due to luck, and thus it is a statistically significant result because it suggests a shift away from the null hypothesis.

If this turns out to be true, i.e. p value is less than sig level, then you reject the null hypothesis as it is not longer a suitable statement. You do not accept the alternate hypothesis however either as you need to be careful.

P.S. This might help you understand a bit more: https://opentextbc.ca/researchmethod...hesis-testing/
Thank you so much! I think I understand it now.

So just to clarify that my understanding is correct, with the example that I attached, when the probability of having faulty articles is less than or equal to 8% is less than 5%, we say that this probability is too small to have occurred by chance, and so we accept that it is statistically significant, so accepting the alternate hypothesis, which in this case is to say that the probability of faulty articles is less than 10%.
Last edited by Kitten261002; 2 months ago
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