**HL Maths P2 Before/After

MathsManiac

ehshup wrote: »

If you are told that 330/1100 people like Yummy Cola, and a month later you conduct a survey of your own and find that 95/250 people like it. Can you say with 95% confidence that more people like Yummy Cola now?

Now with a question like that (one of which came up in our mock), the margin of error was only used once in the marking scheme as follows:
population proportion = 330/1110 = .3 or 30%
sample proportion p = 95/250 = .38 or 38 %
Margin of error = 1/√250 = .063
Confidence interval = .317 < p < .443
Population proportion, .3, is not within confidence interval, hence one can conclude that more people do like Yummy cola.

Now I have a problem with this solution, because it didn't take into account the possible error in the first test:
Margin of error for first = 1/√1100 = .03
hence the confidence interval for the first is .27 < p < .33
and so it is possible that the amount of people who like Yummy cola is the same, as the confidence interval for one overlaps the confidence interval for the other.
While I made this question up off the top of my head, the question in our mock was almost the same, however I got no marks for it because I calculated margin of error for the first. Can anyone confirm what the right thing to do is in this situation?

Your reservations about this question are valid, assuming the first piece of information was also a sample. (If the 1100 people at the start was the full population of interest, and the later sample is a sample of 250 people out of that group, then you could argue the question was o.k.)

Doing a hypothesis test for a difference between two populations based on a sample from each is more complicated, and well beyond the LC syllabus. If you REALLY want to know how to do it, I suggest you wait until your exams are a happy memory, and then Google: "hypothesis test for difference between population proportions". First hit is this: http://stattrek.com/hypothesis-test/difference-in-proportions.aspx, which looks ok to me.

Bottom line: the question was poorly phrased, so don't worry about it.

Edit: RedTexan beat me to it!

IRA 1916

hamal wrote: »

What are ye doin for q6? learnin theorems 11,12 and 13 and hopin for the best?

Also are ye all learning the derivations of the trig formulae? awful lot of work for something that has never been in an SEC paper/sample paper!:rolleyes:

More reason to put em in

CareNone17

mcpaddington wrote: »

So are these the only things that we have to be able to prove?
Theorem 11, 12 and 13.
Trig formulas 1-7 and 9.

Is it really just these that they'll be asking us? and Proof of Contradiction?

Mista

hamal wrote: »

What are ye doin for q6? learnin theorems 11,12 and 13 and hopin for the best?

Also are ye all learning the derivations of the trig formulae? awful lot of work for something that has never been in an SEC paper/sample paper!:rolleyes:

Theorums, sin graphs, proof by contradiction... think thats it.. not gna bother with the formulae proofs

hamal

Mista wrote: »

Theorums, sin graphs, proof by contradiction... think thats it.. not gna bother with the formulae proofs

sin graphs i'd say are guaranteed q5 just hav the feeling.. and yeh but if i dont learn the proofs and one comes up i'll be fairly ragin haha

Mista

hamal wrote: »

sin graphs i'd say are guaranteed q5 just hav the feeling.. and yeh but if i dont learn the proofs and one comes up i'll be fairly ragin haha

:O they're in Q5? Frig.. might have a look at them then.. wouldn't like to be stuck with a proof and a geometry question

hamal

Mista wrote: »

:O they're in Q5? Frig.. might have a look at them then.. wouldn't like to be stuck with a proof and a geometry question

Well hold on, by 'sin graphs' i presume you mean having to do the graph of sin(x) just like Q5 in the 2011 sample paper or similar type q's?

Just hoping the marking scheme is nice and generous and that theorem 11 pops up in question 6 even though it was there last year:(

Mista

hamal wrote: »

Well hold on, by 'sin graphs' i presume you mean having to do the graph of sin(x) just like Q5 in the 2011 sample paper or similar type q's?

Just hoping the marking scheme is nice and generous and that theorem 11 pops up in question 6 even though it was there last year:(

Yea, i thought they were Q6 for some reason..

hamal

Mista wrote: »

Yea, i thought they were Q6 for some reason..

Nope Q5, hope they come up easy marks in my opinion

Dapics

hamal wrote: »

Nope Q5, hope they come up easy marks in my opinion

Dont forget about the general equation....

Very easy question.

The no in front of the trig identity is the range and the number behind the trig identity is the period.

Range = How Far up/down the graph goes (Y value)
Period = How many times it goes up/down in 180 degress

Usually the period will be two, so it will go up and down twice before hitting 180 degrees.

DepoProvera

Dapics wrote: »

Dont forget about the general equation....

Very easy question.

The no in front of the trig identity is the range and the number behind the trig identity is the period.

Range = How Far up/down the graph goes (Y value)
Period = How many times it goes up/down in 180 degress

Usually the period will be two, so it will go up and down twice before hitting 180 degrees.

Tthe period is the sort of 'building block' of the graph, it's the bit that gets repeated. Periods will never be numbers like "2" they'll be 90 degrees etc. To find the period from eg f(x)=sin3x you go 360/3=120 degrees... at least that's what I was taught anyway :P

cocopopsxx

Need a little help here. Do you know for thr sin graphs, how to know whose sine we have to take? Like 0,pi,pi/2 etc. How to figure this out?

And I'll be leaving Q8 blank cos I just can't do trig no matter how hard I try. anything I can do?

And are ye learning all the constructions?

DepoProvera

Lads definitions: definition, axiom, theorem, proof, corollary, proposition, implies, converse, is equivalent to, if and only if... Am I missing any/are these correct?

paddyhes

cocopopsxx wrote: »

Need a little help here. Do you know for thr sin graphs, how to know whose sine we have to take? Like 0,pi,pi/2 etc. How to figure this out?

And I'll be leaving Q8 blank cos I just can't do trig no matter how hard I try. anything I can do?

And are ye learning all the constructions?

this video explains trig functions well and should be part of a playlist.
http://www.youtube.com/watch?v=vHYI93UV5Kg

finality

DepoProvera wrote: »

Tthe period is the sort of 'building block' of the graph, it's the bit that gets repeated. Periods will never be numbers like "2" they'll be 90 degrees etc. To find the period from eg f(x)=sin3x you go 360/3=120 degrees... at least that's what I was taught anyway :P

I think they meant 2pi

though dapics, your definition of the period is inaccurate

the period of a sin(x) or cos(x) graph is 2pi
the period of sin(2x) would be pi
sin(3x) is 2pi/3

etc

and what it is is how often the graph repeats itself. So between 0 and 2pi the graph of six(x) would start at 0, go up to 1 once, down to -1 once, and come back up to 0.

ChemHickey

finality wrote: »

I think they meant 2pi

If you want a formula for the graphs.. :L


asinbx = graph

[-a,a] = range

2pi/b = period.


eg 2sin4x has a range of [-2,2] and a period of pi/2

leaveiton

You know for things like axioms? Do we need to know any particular axioms or do we just need to know what an axiom is?

finality

ChemHickey wrote: »

If you want a formula for the graphs.. :L


asinbx = graph

[-a,a] = range

2pi/b = period.


eg 2sin4x has a range of [-2,2] and a period of pi/2

Haha, well I know that. Why'd you quote my post? :L

leaveiton

Another question, if we're asked for a construction do we need to write out all the steps (e.g. draw a line AB, put the compass on point A, etc) or do we simply construct?

RedTexan

leaveiton wrote: »

You know for things like axioms? Do we need to know any particular axioms or do we just need to know what an axiom is?

there is exactly one line that passes through any two points

ChemHickey

finality wrote: »

Haha, well I know that. Why'd you quote my post? :L

I didn't mean to.. I was on my phone... But incase you didn't like...

leaveiton

RedTexan wrote: »

there is exactly one line that passes through any two points

Do we need to know that/is that all we need to know?

I'm sorry about all the questions, but my teacher has told us nothing about any of this.

DepoProvera

leaveiton wrote: »

Another question, if we're asked for a construction do we need to write out all the steps (e.g. draw a line AB, put the compass on point A, etc) or do we simply construct?

No you don't, but I tend to label the circumcentre etc

ChemHickey

RedTexan wrote: »

there is exactly one straightline that passes through any two points

Jeeeez. :P

Nazata

Do we need to prove any converses and/or know a definition for the converse of a theorem?

ChemHickey

Are people using their calculators to find the line-of-best-fit?

If so, how do you do it on a Sharp

ChemHickey

Nazata wrote: »

Do we need to prove any converses and/or know a definition for the converse of a theorem?

Yes, and yes. But I'd say they'd only give that to us in Q6A with a specific theorem.

ehshup

ChemHickey wrote: »

Are people using their calculators to find the line-of-best-fit?

If so, how do you do it on a Sharp

refer to http://inside.lambton.on.ca/Nav/index_html?RECORDID=1408&TYPE=28

emmamurphy233

DepoProvera wrote: »

Lads definitions: definition, axiom, theorem, proof, corollary, proposition, implies, converse, is equivalent to, if and only if... Am I missing any/are these correct?

Does anybody know where I can find definitions for these? My teacher was useless and i didn't even know we had to know these until I saw it here..

ehshup

emmamurphy233 wrote: »

Does anybody know where I can find definitions for these? My teacher was useless and i didn't even know we had to know these until I saw it here..

Google...i'm not joking