MATH2901 Higher Theory of Statistics (1 Viewer)

[InteGrand]

I think you forgot to divide by the determinant of the Fisher Information Matrix. You appear to have multiplied by it (or something).

 

[InteGrand]

Also I think the final answer's denominator should be n^2 (not n).

 

[Flop21]

Any tips on what test statistic to use for a hypothesis test?

 

[InteGrand]

Any tips on what test statistic to use for a hypothesis test?

It depends on the hypothesis test and the situation at hand. Common ones are when you have asymptotic normality under a null hypothesis (which is often the case from the Central Limit Theorem), you can use a Z-test ( https://en.wikipedia.org/wiki/Z-test ), or you could use a Chi-Squared test sometimes. Depends on what purpose the test is serving.

 

[leehuan]

Also I think the final answer's denominator should be n^2 (not n).

Oh I double checked that. I put the n back in there, got a determinant of (2alpha beta^2)/n^2 * (a matrix with n's appearing everywhere). That's fine I reckon

Any tips on what test statistic to use for a hypothesis test?

When we were taught it, we were honestly taught "educated guess". Normally I try to exploit the CLT.

 

[InteGrand]

Oh I double checked that. I put the n back in there, got a determinant of (2alpha beta^2)/n^2 * (a matrix with n's appearing everywhere). That's fine I reckon



When we were taught it, we were honestly taught "educated guess". Normally I try to exploit the CLT.

Oh yeah, I forgot to include the n in front of the matrix when getting the 1,1 entry of the inverse. It should be n in the denominator indeed (for final answer).

 

[Flop21]

Can you guys help me with going through this question:

So to start off, is the null and alternative hypothesis.... H0 = 95 versus H1 < 95. Or is this wrong??

OR is it H0 < 95 versus H1 >= 95

 

[Flop21]

nvm

 

[InteGrand]

Also I read that if standard deviation / sigma is know, we can use z-distribution. If not, use t-distribution. We're given the sample SD right?? Does that mean we know it or not?

We don't know it ("it" refers to the population standard deviation (or really the standard deviation of the assumed underlying distribution)), since that's only the sample standard deviation.

 

[Flop21]

Help pls someone,

So we have to use R commands instead of distribution tables (wtf it's so much easier with the tables)?

How would you then find the region of rejection (when doing a hypothesis test) for both z and t distributions?

E.g. for T test, I would find the degrees of freedom (n-1), and look up n-1 on the T table with the respective value of alpha, say 0.05. How would you do this in the test????

 

[leehuan]

Help pls someone,

So we have to use R commands instead of distribution tables (wtf it's so much easier with the tables)?

How would you then find the region of rejection (when doing a hypothesis test) for both z and t distributions?

E.g. for T test, I would find the degrees of freedom (n-1), and look up n-1 on the T table with the respective value of alpha, say 0.05. How would you do this in the test????

You leave it there. They will supply you the R code and all you have to do is read it.

Since you do computer science you shouldn't have any trouble understanding just one line of code tbh

 

[Flop21]

You leave it there. They will supply you the R code and all you have to do is read it.

Since you do computer science you shouldn't have any trouble understanding just one line of code tbh

yeah I am a mind reader that knows what vaguely named functions do


But anyway I know it's just going to be a shit show. Hopefully not, but I am 80% sure it will be.

 

[leehuan]

yeah I am a mind reader that knows what vaguely named functions do


But anyway I know it's just going to be a shit show. Hopefully not, but I am 80% sure it will be.

R's free to download. You can always just investigate briefly

Here's an example of something that might appear

Tbh all I've seen is p___, q___, r___ where ___ is a distribution.
p - probability
q - quantile
r - just a bunch of random simulations

 

[Flop21]

R's free to download. You can always just investigate briefly

Here's an example of something that might appear

Tbh all I've seen is p___, q___, r___ where ___ is a distribution.
p - probability
q - quantile
r - just a bunch of random simulations

Thanks

tbh I think I will fail this course unfortunately

 

[kawaiipotato]

Thanks

tbh I think I will fail this course unfortunately

You could try the 2901 exam past papers just in case, as they seem to be similar difficulties (I think some questions overlap? or the old ones used to anyway.)

 

[BenHowe]

All this stat stuff looks so much more complicated than what I've done. Only done stat171 where had z, various t tests, and chi squared test for independence and GOF test... rip

 

[kawaiipotato]

All this stat stuff looks so much more complicated than what I've done. Only done stat171 where had z, various t tests, and chi squared test for independence and GOF test... rip

We learn this in second year at UNSW, so it seems a bit later than at Macquarie.

 

[BenHowe]

Can you guys help me with going through this question:

So to start off, is the null and alternative hypothesis.... H0 = 95 versus H1 < 95. Or is this wrong??

OR is it H0 < 95 versus H1 >= 95

I think youre supposed to make the null hypothesis equal to something but it doestn really matter so I guess

This is how I would do it

 

[i1337]

I think youre supposed to make the null hypothesis equal to something but it doestn really matter so I guess

This is how I would do it

I think it should be Ho: U = 95, Ha: U < 95

R output is mainly qnorm / pnorm / qt IIRC. Qnorm is % shaded eg qnorm(0.5) = 0 i.e. 50% shaded is at 0 on the normal distribution, etc. Pnorm is opposite so Pnorm(0.5) = the % shaded at z = 0.5 (or the pnorm/qnorm may have been other way around)