S2 hypotheses testing

Angels1234

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I don’t understand what’s the difference between the significance level at critical region . What do each of them mean ?

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Shaanv

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(Original post by Angels1234)
I don’t understand what’s the difference between the significance level at critical region . What do each of them mean ?

Sorry im not quite sure what u mean. Could u clarify? Maybe post a question and show what u are referring to?

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Angels1234

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(Original post by Shaanv)
Sorry im not quite sure what u mean. Could u clarify? Maybe post a question and show what u are referring to?

Sorry I made a mistake . I just meant the difference between the significance level and critical region

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Gregorius

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(Original post by Angels1234)
Sorry I made a mistake . I just meant the difference between the significance level and critical region

The critical region consist of those values of your test statistic for which you would reject the null hypothesis.

The significance level is a threshold of probability below which you would reject the null hypothesis. The probability in question is the probability of obtaining the observed value of the test statistic, or a more extreme value, conditional upon the null hypothesis being true.

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Angels1234

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(Original post by Gregorius)
The critical region consist of those values of your test statistic for which you would reject the null hypothesis.

The significance level is a threshold of probability below which you would reject the null hypothesis. The probability in question is the probability of obtaining the observed value of the test statistic, or a more extreme value, conditional upon the null hypothesis being true.

what do we mean about test statistic .. is it like the population mean or variance . Only problem is that isnt mu and sigma unknown parameters so how are they statistics ?

Is the critical region just like a region in which you would reject the null hypothesis . So if the critical value was say 1.6449 then any value above tthis in a one tail ttest would mean we reject the null hyp. When doing hypothesis tests and when we get a Z value based what exactly does this tell us . Like what does the Z value we calculate represent ?

Is it correc too sat that the critical region is defined by the critical values and the critical values depend on what the significance level is

thank you

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Sinnoh

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I'll use an example. Say your significance level is 5%. That tells you, if the probability of the event is less than that, then something is not quite right and you should reject the null hypothesis.

The critical region refers to "What are the values of your random variable, for which the probability of that happening is less than 5%?

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Gregorius

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(Original post by Angels1234)
what do we mean about test statistic .. is it like the population mean or variance . Only problem is that isnt mu and sigma unknown parameters so how are they statistics ?

A "statistic" is any function of your sample data. So the mean of a sample, or its standard deviation, is a statistic. We use the terminology "test statistic" when we're using a statistic (like the sample mean) to perform a hypothesis test.

Is the critical region just like a region in which you would reject the null hypothesis . So if the critical value was say 1.6449 then any value above tthis in a one tail ttest would mean we reject the null hyp.

Yes, that's it.

When doing hypothesis tests and when we get a Z value based what exactly does this tell us . Like what does the Z value we calculate represent ?

It tells you "where" in the normal probability distribution you are. Typically the hypothesis tests you'll do will all use the normal distribution - so your critical regions will be out in the tails of the normal distribution - i.e large negative or positive Z values.

Is it correc too sat that the critical region is defined by the critical values and the critical values depend on what the significance level is

Yes. (Although, at a more advanced level, you need some more assumptions for this to work).

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Gregorius

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(Original post by Sinnoh)
I'll use an example. Say your significance level is 5%. That tells you, if the probability of the event is less than that, then something is not quite right and you should reject the null hypothesis.

The critical region refers to "What are the values of your random variable, for which the probability of that happening is less than 5%?

Ummmm, No, not quite.

The basis of a hypothesis test is that you work out the probability of observing some value, or a more extreme value, of a test statistic of some sort.

So, for example, if the hypothesis is that the population mean is zero, then you work out the value of the mean of a sample, turn that into a z-value and from thence get a p-value. That p-value is the probability (assuming the null hypothesis to be true) of observing that value of the sample mean or a value more extreme than that observed.

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Angels1234

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(Original post by Gregorius)
Ummmm, No, not quite.

The basis of a hypothesis test is that you work out the probability of observing some value, or a more extreme value, of a test statistic of some sort.

So, for example, if the hypothesis is that the population mean is zero, then you work out the value of the mean of a sample, turn that into a z-value and from thence get a p-value. That p-value is the probability (assuming the null hypothesis to be true) of observing that value of the sample mean or a value more extreme than that observed.

Okay wait sorry I’m still stuck again . I think I’m getting mixed up in s3 now . In s3 in ch3 hypothesis testing we get a value for Z and we compare it to the critical value and from the we reject or accept the null hypothesis. After we get the Z value in s2 why can’t we compare it to the critical value which depends on the significance level and reject or accept the null hypothesis depending

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Gregorius

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(Original post by Angels1234)
Okay wait sorry I’m still stuck again . I think I’m getting mixed up in s3 now . In s3 in ch3 hypothesis testing we get a value for Z and we compare it to the critical value and from the we reject or accept the null hypothesis. After we get the Z value in s2 why can’t we compare it to the critical value which depends on the significance level and reject or accept the null hypothesis depending

I might have to pass this over to someone who teaches this stuff, as I don't know what's where at A-level! Notnek ?

But my criticism of the post quoted is that hypothesis tests are performed on the basis of the probability of an event - the particular value of a test statistic. I'm afraid they're not (and that's the beginning of a loooong story!) they're based on the probability of the test statistic taking a particular observed value, or a value more extreme than that observed.

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Notnek

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(Original post by Gregorius)
I might have to pass this over to someone who teaches this stuff, as I don't know what's where at A-level! Notnek ?

Unfortunately I've never taught old spec so can't help with questions about S1/2/3 etc.

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Angels1234

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(Original post by Gregorius)
I might have to pass this over to someone who teaches this stuff, as I don't know what's where at A-level! Notnek ?

But my criticism of the post quoted is that hypothesis tests are performed on the basis of the probability of an event - the particular value of a test statistic. I'm afraid they're not (and that's the beginning of a loooong story!) they're based on the probability of the test statistic taking a particular observed value, or a value more extreme than that observed.

I’m feeling quite confused rn

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Notnek

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(Original post by Angels1234)
Okay wait sorry I’m still stuck again . I think I’m getting mixed up in s3 now . In s3 in ch3 hypothesis testing we get a value for Z and we compare it to the critical value and from the we reject or accept the null hypothesis. After we get the Z value in s2 why can’t we compare it to the critical value which depends on the significance level and reject or accept the null hypothesis depending

Can you explain how it's done in S2?

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Addidashoodie

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Basically in simple terms the significance level sets a boundary where if your data exceeds it then it falls in to the critical region and your null hypothesis is rejected

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Addidashoodie

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(Original post by Notnek)
Can you explain how it's done in S2?

This is

(Original post by Notnek)
Can you explain how it's done in S2?

For S2 you look at your binomial distribution table. I think that's what he means by Z value

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Angels1234

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(Original post by Notnek)
Can you explain how it's done in S2?

Haven’t done s2 in a while so can’t really remember no .
https://postimg.org/image/7lchf2gh9/

Why do we have to work out p(Z>1.87) why can’t we say well 1.87 is bigger than the critical value of 1.6449 (the Z value that corresponds to 5 percent significance level ) therefore reject h0 and accept claim

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Gregorius

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(Original post by Angels1234)
Haven’t done s2 in a while so can’t really remember no .
https://postimg.org/image/7lchf2gh9/

Why do we have to work out p(Z>1.87) why can’t we say well 1.87 is bigger than the critical value of 1.6449 (the Z value that corresponds to 5 percent significance level ) therefore reject h0 and accept claim

Again, I'll leave it to those who teach this stuff to explain why it's taught this way...

...but these are equivalent approaches. Perhaps the point is that the number 1.644 has to come from somewhere - why do you use it? You use it because the probability of a standard normal random variable being greater than 1.644 is 0.05. So the critical region of z > 1.644 corresponds to a (one sided) p-value of less than 0.05.

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