Hypothesis testing- Statistics Watch

Al4stair
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https://media.discordapp.net/attachm...600&height=278

b) The question outlines that the significance level is 2.5%. The significance level is the probability of rejecting the the null hypothesis when it is true. So, isn't the correct answer to b), 2.5%?

(2.5% is not the answer given by the source)
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Pangol
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(Original post by Al4stair)
https://media.discordapp.net/attachm...600&height=278

b) The question outlines that the significance level is 2.5%. The significance level is the probability of rejecting the the null hypothesis when it is true. So, isn't the correct answer to b), 2.5%?

(2.5% is not the answer given by the source)
As this is a two-tailed test, where the probability in each tail is ideally 2.5%, the significance level for the whole test is 5%, as that would be the chance of falling into one tail or the other.

But in reallity, the probability of falling into one tail or the other is unlikely to be exactly 5%. You need to add the actual probabilities of falling into one tail or the other to get the actual significance level. You would have had to find the probabilities in (a) when you made sure that the probability in each tail is as close as possible to 2.5%.
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Al4stair
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(Original post by Pangol)
As this is a two-tailed test, where the probability in each tail is ideally 2.5%, the significance level for the whole test is 5%, as that would be the chance of falling into one tail or the other.

But in reallity, the probability of falling into one tail or the other is unlikely to be exactly 5%. You need to add the actual probabilities of falling into one tail or the other to get the actual significance level. You would have had to find the probabilities in (a) when you made sure that the probability in each tail is as close as possible to 2.5%.
Ok. Thanks for explaining. But do you know why the significance level is defined as the probability of rejecting H0 when it is true, since for part b) you get 4.3%, but the significance level, as you said, is 5%?
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Pangol
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(Original post by Al4stair)
Ok. Thanks for explaining. But do you know why the significance level is defined as the probability of rejecting H0 when it is true, since for part b) you get 4.3%, but the significance level, as you said, is 5%?
You can think of the 5% significance level that you are set in the question as the "nominal" significance level - in an ideal world, you would like there to be a 5% chance of falling into the two tails. But this is a discrete distribution, needing a discrete cut-off point for doing so, and therefore the actual probability of falling into the tails is not 5% - you say that it is 4.3% in your case. So, there is actually a 4.3% probability that an observation from your distribution would fall into the tails, and as that is your criteria for rejecting H0, there is therefore a 4.3% chance that you will reject H0 when it is true.

[Although I have some memory of someone more knowledgeable that I pointing out in the past that it doesn't quite work like this, although this interpretation is fine for A Level.]
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Al4stair
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(Original post by Pangol)
You can think of the 5% significance level that you are set in the question as the "nominal" significance level - in an ideal world, you would like there to be a 5% chance of falling into the two tails. But this is a discrete distribution, needing a discrete cut-off point for doing so, and therefore the actual probability of falling into the tails is not 5% - you say that it is 4.3% in your case. So, there is actually a 4.3% probability that an observation from your distribution would fall into the tails, and as that is your criteria for rejecting H0, there is therefore a 4.3% chance that you will reject H0 when it is true.

[Although I have some memory of someone more knowledgeable that I pointing out in the past that it doesn't quite work like this, although this interpretation is fine for A Level.]
Ok. Thankyou for explaining.
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