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# The Official Edexcel S2 Revision Thread! (22/06/05 PM) watch

1. How do they get 0.2632? Why would they double 0.1316?
2. PerkyDani-

Significance level is the lowest level of probability acceptable for an event to occur under the null hypothesis if the null hypothesis is to remain. If the probability of an event that occured is less likely than the significance level, then you have reason to suggest that the null hypothesis is incorrect
3. does anyone have the mark scheme for the mock paper??? i have now done all of the past papers i have and am beginning to panic more...
my main problem is stupid mistakes and not understanding the questions!
4. *Mock Paper answers*

1. a) Straight line, from 0 to 6 on the x-axis, going up to 1/7 on the y-axis
Straight horizontal line from 6 to 10 on the x-axis
Bolded straight line showing f(x) = 0, when x<0

b) 59/84
c) 0.507

2. a) 0.08
b) 0.3
c) 0.0473
d) 0.1425, accept 0.143

3. a) D is continuous
b) Sampling frame is the list of competitors or their results, e.g. label the results 1-200 and randomly select 36 of them
c) 0.004
d) Probability is very low, so assumption of P(A=2) = 1/3, is unlikely.
(Suggests P(A=2) might be higher)

4. a) Critical region is X<0 , or X>7
b) 0.067
c) P(Y>14) = 0.0835
Not significant. Insuffcient evidence of an increase in the rate of sales.

5. a) k = 16/27
b) 11/27
c) f(t):
(32/27)(6t² - 4t³) , 0<t<1.5
0 , otherwise

d) 0.9
e) 0.4752
f) 0.7763 (accept 0.776)

6. a) 0.3528
b) P(Y<7) = 0.3239
c) 0.59866 (accept 0.599)
d) 0.9554 (accept 0.955 ir 0.956)

[Any mistakes, then tell me, so I can check again]
5. Jeeez I dislike S2 its the only Maths module I dislike.
6. Does anyone have any decent notes on hypothesis testing? I can do about half of it now where you have a basic binomial or poisson situation and want to determine if something has increased or decreased. However, some things still confuse me such as when you have to use a normal approximation with a hypothesis test, etc.

Also, could someone please explain how to do question 3 from the January 2005 paper? I couldn't do any of it when I attempted the paper this evening.
7. Ok rectangular distribution.. i wasnt in when this was taught and all i know is the formulas for mean and variance but this doesnt seem to help here. My problem is with c) and d)

This is from Solomon Paper B btw..

3) In a test studying reaction times, white dots appear at random on a black rectangular screen. The continuous random variable X represents the distance, in centimetres, of the dot from the left hand edge of the screen. The distribution of X is rectangular over the interval [0,20].

a) Find P(2<X<3.6).
ok i got 0.08 for this

b) Find the mean and variance of X.
mean i got 10, variance i got 33.25

The continuous random variable Y represents the distance, in centimetres, of the dot from the bottom edge of the screen. The distribution of Y is rectangular over the interval [0,16].

Find the probability that a dot appears

c) in a square of side 4 cm at the centre of the screen

d) within 2 cm of the edge of the screen

I attempted them (poorly i believe) n got 1/4 and 1/8 but id appreciate if sumone who knew wat they were doin helped me out.

Thx in advance
8. (Original post by Featherflare)

The continuous random variable Y represents the distance, in centimetres, of the dot from the bottom edge of the screen. The distribution of Y is rectangular over the interval [0,16].

Find the probability that a dot appears

c) in a square of side 4 cm at the centre of the screen

d) within 2 cm of the edge of the screen

I attempted them (poorly i believe) n got 1/4 and 1/8 but id appreciate if sumone who knew wat they were doin helped me out.

Thx in advance

(c) = 4/16 x 4/20 = 16/320 = 1/20

(d) = 4/16 + 4/20 -16/320 = 128/320 = 8/20

If in doubt, draw a rectangle, and imagine squares of probability, with the whole area being 1...helps to visualise i.e. with part (c), a 4x4 square takes up 16 bits of the 16x20 rectangle

with (d), do the side edges, then the bottom and top edges...If you draw a diagram, you will notice that there are overlaps of the slices in each corner of magnitude 4 squares, so overall 16 squares are done twice if you add both sets of slices, so you need to take away the 16 /320 from the summation
9. Thx a lot. Sounds easier than I expected
10. (Original post by KAISER_MOLE)
X-B(20,0.50)

With 10% significance level in a two tailed test, that means basically 5% sig level in two lots of one tailed tests, above and below

=> P(x«7)= 0.1316 <---- too high, no rejection

=> P(x»7) = 1-P(x«6) = 0.9423 <------definitely no rejection

They write the answer in the back of the book as 0.2632 , so I guess that is just double the lowest probability.... o____0
Yea there are two ways of doing that. Either by finding P(X«7) (as bad as or worse) and doubling it because it is a two tailed test and is split both ways (in this case 5% each way) OR by finding the critical regions and therefore determining whether 7 is inside. Strictly speaking the critical regions is how it should be done
ie. P(X<C1 ) = 0.05
P(X>C2 ) = 0.05 and so P(X«C2-1 ) = 0.95
and find the x values closest to these probabilities (by checking stat tables)while assuring that they make up for each other (ie. if one is a little too high look for the other to be a little too low)
However both methods are accepted so its usually safer to use the first method as it's easier
11. (Original post by Chris87)
However, some things still confuse me such as when you have to use a normal approximation with a hypothesis test, etc.
Do we have to know that for the Edexcel S2 exam?? I only got taught hypothesis testing using binomial and poisson and that's the only two in the text book.

(Original post by Chris87)
Also, could someone please explain how to do question 3 from the January 2005 paper? I couldn't do any of it when I attempted the paper this evening.
Are you talking about this question:

'A rod of length 2l was broken into 2 parts. The point at which the rod broke is equally likely to be anywhere along the rod. The length of the shorter piece of rod is represented by the random variable X.

(a) write down the name of the probabily density function of X, and specify it fully. (3 marks)

(b) Find P(X < 1/3 l) (2 marks)

(c) Write down the value of E(X) (1 mark)

Two identical rods of length 2l are broken
(d) Find the probability that both of the shorter pieces are of length less than 1/3 l (2 marks)"

I know it's a continuous uniform distribution but I've forgotten how to work out the pdf. I've got the answers which my teacher wrote but I don't get how he got the pdf (it's 1/l for 0 <= x <= l and 0 otherwise) - probably because I've forgotten how to do these questions!

part b) is 1/3 and c) is ½l and d) is 1/9

Can anyone explain this question to me please?
12. not done S2 in ages! - gonna revise it this weekend - some aspects esp the hypothesis testing and when to use which distribution is ahrd - hate that

pk
13. (Original post by bbcer)
Do we have to know that for the Edexcel S2 exam?? I only got taught hypothesis testing using binomial and poisson and that's the only two in the text book.
That's what I thought but then I found the following question from the January 2005 paper:

In an experiment, there are 250 trials and each trial results in a success of a failure.

a) Write down two other conditions needed to make this into a binomial experiment.

It is claimed that 10% of students can tell the difference between two brands of baked beans. In a random sample of 250 students, 40 of them were able to distinguish betweeen the difference between the two brands.

b) Using a normal approximation, test at the 1% level of significance whether or not the claim is justified. Use a one-tailed test.

c) Comment on the acceptability of the assumptions needed to carry out the test.

Part a is obviously easy but part b was the one that confused me.

(Original post by bbcer)
Are you talking about this question:
Yes, that's the question.
14. (Original post by Chris87)
That's what I thought but then I found the following question from the January 2005 paper:

In an experiment, there are 250 trials and each trial results in a success of a failure.

a) Write down two other conditions needed to make this into a binomial experiment.

It is claimed that 10% of students can tell the difference between two brands of baked beans. In a random sample of 250 students, 40 of them were able to distinguish betweeen the difference between the two brands.

b) Using a normal approximation, test at the 1% level of significance whether or not the claim is justified. Use a one-tailed test.

c) Comment on the acceptability of the assumptions needed to carry out the test.

Part a is obviously easy but part b was the one that confused me.
I didn't know that! Just tried doing it...

I worked out the mean for the normal dist which is np = 25 and the variance is 250 x 0.1 x 0.9 = 22.5

so X ~ B(250, 0.1) ≈ Y~N(25,22.5)

Let p represent proportion of students who can distinguish between brands

H0: p=0.1 and H1>0.1

I assume this is what my teacher did (it's not really clear what he's done):
P(X => 40) ≈ P(Y > 39.5) (applying the half continuity correction)
= P(Z > (39.5 - 25)/√22.5)
= P(Z > 3.056...)
= 1 - Φ(3.05)
= 1 - 0.9989
= 0.0011 < 10% so the claim cannot be accepted

Think that's how you would answer it - can someone check it please. I don't get part c).
15. (Original post by Chris87)
It is claimed that 10% of students can tell the difference between two brands of baked beans. In a random sample of 250 students, 40 of them were able to distinguish betweeen the difference between the two brands.

b) Using a normal approximation, test at the 1% level of significance whether or not the claim is justified. Use a one-tailed test.

c) Comment on the acceptability of the assumptions needed to carry out the test.
Just noticed a post on my thread on hypothesis testing where someone has answered the above question:
http://www.thestudentroom.co.uk/show...2&postcount=11
don't get what the person did though
16. for normal distribution approximations, do you need to INTERPOLATE for edexcel?
17. As far as i am aware, interpolation is not required..
18. I was just wondering when your doing a PDF or CDF. The mark scheme usually factorises it. I usually don't factorise it, but my answer is correct. Will i loose any marks?

Also when finding the CDF, the mark scheme does the X0 way, but i use the method of finding C another way sometimes. Again though it's the same answer, but will i loose marks?
19. Could someone please remind me of everything they can ask us on hypothesis testing?
20. They can ask you an awful lot, although it is mainly just null and alternative hypothesis

This can be a one or two tailed test, though if it is a two tailed test the question is likely to give you a few prompts (i.e, to take significance level on each tail as close to 2.5% as possible)....there's not much to hypothesis testing really, learning the definitions from the chapter is a must, you do that and you will jump up at least half a grade...

edit: Oh my god my lemon sorbet has melted and is seperating out...I am not happy with this

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