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# MEI S3 2016 Unofficial Mark Scheme

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1. Q2 (i) (9 marks) (Goodness of Fit): Critical Value: 9.348, Test Statistic: 5.017
Not significant, some evidence to suggest model fits data.

Q2 (ii) (9 marks) (Wilcoxon Signed Rank): Critical Value: 17, Test Statistic: 16
Significant, some evidence to suggest median wing length of fruit flies is greater for South American fruit flies compared to European fruit flies.

Q3 (i) Through integration of f(x)=1, k=3/4
Q3 (ii) Var(X) = 1/2 as E(X) = 0
Q3 (iii) Equation was (q^3)-3q+1, substitute 0.35 in to get approx. 0.
Q3 (iv) Normal distribution as n is large and so data will tend towards central limit theorem. Value of 0.7892.

Q4 (i) (A) Both samples may be systematically biased.
(B) Individual samples may not be representative.
Q4 (ii) (10 marks) (t-test): Critical Value: 1.833, Test Statistic: 1.067
Not significant, insufficient evidence to suggest a mean decrease in time taken on the whole.
Q4 (iii) Assumption: The population mean (1) of differences (1) follows an approximate normal distribution (1).
Q4 (iv) Confidence interval of (-1.85, 4.85) (I think, something like that)

If anyone can add Question 1 on (or correct any of the above) I'd be grateful as all I remember is (i) being phi(0.5), I've forgotten all the others! Thanks!
Q2 (i) (9 marks) (Goodness of Fit): Critical Value: 9.348, Test Statistic: 5.017
Not significant, some evidence to suggest model fits data.

Q2 (ii) (9 marks) (Wilcoxon Signed Rank): Critical Value: 17, Test Statistic: 16
Significant, some evidence to suggest median wing length of fruit flies is greater for South American fruit flies compared to European fruit flies.

Q3 (i) Through integration of f(x)=1, k=3/4
Q3 (ii) Var(X) = 1/2 as E(X) = 0
Q3 (iii) Equation was (q^3)-3q+1, substitute 0.35 in to get approx. 0.
Q3 (iv) Normal distribution as n is large and so data will tend towards central limit theorem. Value of 0.7892.

Q4 (i) (A) Both samples may be systematically biased.
(B) Individual samples may not be representative.
Q4 (ii) (10 marks) (t-test): Critical Value: 1.833, Test Statistic: 1.067
Not significant, insufficient evidence to suggest a mean decrease in time taken on the whole.
Q4 (iii) Assumption: The population mean (1) of differences (1) follows an approximate normal distribution (1).
Q4 (iv) Confidence interval of (-1.85, 4.85) (I think, something like that)

If anyone can add Question 1 on (or correct any of the above) I'd be grateful as all I remember is (i) being phi(0.5), I've forgotten all the others! Thanks!
Confidence interval false, Var(X)=0.2, you've forgotten the sketch pdf question, I think 1 i) was 1-0.8413=0.1587, Wilcoxon is correct, 3iv) also false.
3. (Original post by notanooblol)
Confidence interval false, Var(X)=0.2, you've forgotten the sketch pdf question, I think 1 i) was 1-0.8413=0.1587, Wilcoxon is correct, 3iv) also false.
Can you remember your t test value?
4. (Original post by decombatwombat)
Can you remember your t test value?

i remember that my mean was -1.06 (or 1.06), standard deviation was 3.4something, do you remember what n was?
5. (Original post by notanooblol)
i remember that my mean was -1.06 (or 1.06), standard deviation was 3.4something, do you remember what n was?
Phew thank god, I got positive 1.06, my t was 0.975 ish, n was 10 if I remember correctly.
6. (Original post by decombatwombat)
Phew thank god, I got positive 1.06, my t was 0.975 ish, n was 10 if I remember correctly.
yeah sounds about right, do you remember what you got for 1) i?
7. (Original post by notanooblol)
yeah sounds about right, do you remember what you got for 1) i?
I know it was 1- the normal table value for 1 (0.8 something), cant remember the exact value
8. (Original post by decombatwombat)
I know it was 1- the normal table value for 1 (0.8 something), cant remember the exact value
yep, so 1-0.8413,
how did you find it? what grade are you aiming for?
9. (Original post by notanooblol)
yep, so 1-0.8413,
how did you find it? what grade are you aiming for?
Aiming for an A, it just seemed a bit strange compared to other papers. Wbu?
10. (Original post by decombatwombat)
Aiming for an A, it just seemed a bit strange compared to other papers. Wbu?
A*, fairly sure that I've secured it after that. What other modules do you do?
11. (Original post by notanooblol)
A*, fairly sure that I've secured it after that. What other modules do you do?
M2 which was like a month ago for some reason, FP2 then the Core maths ones as well. Sorry to ask again, can you remember your Chi Squared Statistic?
12. (Original post by decombatwombat)
M2 which was like a month ago for some reason, FP2 then the Core maths ones as well. Sorry to ask again, can you remember your Chi Squared Statistic?
I took M2 as well, also taaking FP2. Hmm, cant quite remember my number but remember a lot of the numbers so might be able to figure it out. Expected frequencies were: 112.5, 37.5, 37.5, 12.5. Observed frequencies were: 125, 37, do you remember the other observed?
13. (Original post by notanooblol)
I took M2 as well, also taaking FP2. Hmm, cant quite remember my number but remember a lot of the numbers so might be able to figure it out. Expected frequencies were: 112.5, 37.5, 37.5, 12.5. Observed frequencies were: 125, 37, do you remember the other observed?
I think the third one was 31 or 32 but I got those expecteds so we probably got the same answer. I ended up Accepting Ho if I remember right.
14. (Original post by decombatwombat)
I think the third one was 31 or 32 but I got those expecteds so we probably got the same answer. I ended up Accepting Ho if I remember right.

Yeah 32 sounds right, will quickly calculate chi squared
15. (Original post by decombatwombat)
I think the third one was 31 or 32 but I got those expecteds so we probably got the same answer. I ended up Accepting Ho if I remember right.

5.582, do you wanna check question 1 answers as I think i remember question?
16. (Original post by notanooblol)
5.582, do you wanna check question 1 answers as I think i remember question?
Yep 5 something sounds about what I got. And yeah sure, I think the second question was probability of less than 75 minutes. The third was that the 12 middle are 3.5x longer than the 4 Start ones The last one was mean for 12 middle was at least 25 less than the mean for 4 final I think
17. (Original post by decombatwombat)
Yep 5 something sounds about what I got. And yeah sure, I think the second question was probability of less than 75 minutes. The third was that the 12 middle are 3.5x longer than the 4 Start ones The last one was mean for 12 middle was at least 25 less than the mean for 4 final I think
1 ii) variance=10000, mean=4440, P(X<4500)=0.7257

Starting questions x4 mean=200, sd=15
Middle x12 mean=220, sd=25
End x4 mean=250 sd=20
18. (Original post by decombatwombat)
Yep 5 something sounds about what I got. And yeah sure, I think the second question was probability of less than 75 minutes. The third was that the 12 middle are 3.5x longer than the 4 Start ones The last one was mean for 12 middle was at least 25 less than the mean for 4 final I think
19. (Original post by notanooblol)
Exactly what I got apart from I got 0.1198, probably because of the tables. Thanks so much for this, really reassured me in my answers
20. (Original post by decombatwombat)
Exactly what I got apart from I got 0.1198, probably because of the tables. Thanks so much for this, really reassured me in my answers
No worries. I'm glad it went well for us both

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