# Thread: MATH2901 Higher Theory of Statistics

1. ## Re: MATH2901 Higher Theory of Statistics

Originally Posted by leehuan
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).

2. ## Re: MATH2901 Higher Theory of Statistics

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

nvm

4. ## Re: MATH2901 Higher Theory of Statistics

Originally Posted by Flop21
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.

5. ## Re: MATH2901 Higher Theory of Statistics

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????

6. ## Re: MATH2901 Higher Theory of Statistics

Originally Posted by 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????
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

7. ## Re: MATH2901 Higher Theory of Statistics

Originally Posted by leehuan
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.

8. ## Re: MATH2901 Higher Theory of Statistics

Originally Posted by Flop21
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 :P

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

9. ## Re: MATH2901 Higher Theory of Statistics

Originally Posted by leehuan
R's free to download. You can always just investigate briefly :P

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

10. ## Re: MATH2901 Higher Theory of Statistics

Originally Posted by Flop21
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.)

11. ## Re: MATH2901 Higher Theory of Statistics

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

12. ## Re: MATH2901 Higher Theory of Statistics

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

13. ## Re: MATH2901 Higher Theory of Statistics

Originally Posted by 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
I think youre supposed to make the null hypothesis equal to something but it doestn really matter so I guess $H_{0}:\ C\geq\ 95, H_{a}:\ C<95.\text{where C is the cholesterol level}\\ t_{obs}=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\\ t_{obs}=\frac{89.02-95}{\frac{12.9}{\sqrt{6}}}=-1.14\\ \text{Since this is a 1 tail test (note left side), p value}=P(t<-1.14)\\ \text{From the t table and noting DF equals 5, p value}>0.1\\ \text{Assuming alpha is 0.05, at the 5 percent significance level there is insufficient evidence to reject}H_{0}\\ \text{i.e. The blood cholesterol calcium content is greater than or equal to 95 mg/dl for the rat population with 5 percent added fibre to their diets}$

This is how I would do it

14. ## Re: MATH2901 Higher Theory of Statistics

Originally Posted by BenHowe
I think youre supposed to make the null hypothesis equal to something but it doestn really matter so I guess $H_{0}:\ C\geq\ 95, H_{a}:\ C<95.\text{where C is the cholesterol level}\\ t_{obs}=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\\ t_{obs}=\frac{89.02-95}{\frac{12.9}{\sqrt{6}}}=-1.14\\ \text{Since this is a 1 tail test (note left side), p value}=P(t<-1.14)\\ \text{From the t table and noting DF equals 5, p value}>0.1\\ \text{Assuming alpha is 0.05, at the 5 percent significance level there is insufficient evidence to reject}H_{0}\\ \text{i.e. The blood cholesterol calcium content is greater than or equal to 95 mg/dl for the rat population with 5 percent added fibre to their diets}$

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)

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