Question 9:
9 | (a) | H : data consistent with belief, H : not
0 1
Expected frequencies 30, 20, 20, 20, 30
X 2 values 0.1333, 0.8, 0.8, 0.8, 1.2
Total 3.73(333…) (= 51 65 )
< 9.488
Do not reject H . Insufficient evidence that
0
data inconsistent with head’s belief | B1
B1
M1
A1
A1
M1ft
A1ft
[7] | 1.1
1.1
3.4
1.1
1.1
1.1
2.2b | OE, e.g. “follows the given ratio”
Stated or implied
At least two correct, or correct subs in formula
Fully correct
Compare with 9.488, or p = 0.443 > 0.05
Consistent first conclusion, FT on their X 2
Contextualised, not over-definite
Sufficient evidence that belief is correct: A0 | Can be implied by answer
SC: Some cells merged:
can get B2M1A0A0 M1A1
Needs CV 9.488 or 11.14 or 7.815
Withhold A1 if hypotheses reversed
Insuff evidence to reject H0, belief correct M1A1
(b) | “Determine”, so needs proper working
3.73(333…) × n/120 > 9.488
( 7n/225 > 9.488)  n  305 (3 sf)
Must be multiple of 30, so least n is 330 | M1
A1
B1ft
[3] | 3.1b
1.1
3.2a | Inequality for n, using TS and CV
n > 305 or n  305 stated or implied, allow 306
Next multiple of 30 above their 305 | 3.73 gives 305.2, 3.733… gives 304.97
e.g. answer of 305 or 306
Needs reason if rounded up by < 10 or to
multiple of 300
OR | ( 73 n0 − 31 n2 ) 2 ( 43 n0 − 21 n2 ) 2 ( 93 n0 − 31 n2 ) 2
+ 3  +
31 n2 21 n2 31 n2 | M1 | Inequality for n, using 120, TS and CV, needs n
in both O and E terms
() | Or T& I: n = 300 → 9.333 Any n in range
300 to 360, with x 2 in [9.33, 11.2]: M1
n = 330 (9.489) A2 (n = 305 → 9.489 A1)
= 1900 n + 3  1 n + 1 n  9 .4 8 8
150 100
( 7n/225 > 9.488)  n  305 (3 sf) | ( 7n/225 > 9.488)  n  305 (3 sf) | A1 | n > 305 or n  305 stated or implied, allow 306 | e.g. answer of 305 or 306
Must be multiple of 30, so least n is 330 | B1ft | Next multiple of 30 above their 305, needs reason | Or n/120 must be a multiple of 0.25
Inequality for n, using 120, TS and CV, needs n
in both O and E terms
()
Or T& I: n = 300 → 9.333 Any n in range
300 to 360, with x 2 in [9.33, 11.2]: M1
n = 330 (9.489) A2 (n = 305 → 9.489 A1)
A | H : no correlation between variables, H : positive correlation between variables [no context]
0 1 | B0
B | H : no correlation between number of failures and temperature, H : correlation between number of failures and
0 1
temperature [not one-tailed: needs “positive” in H ]
1 | B0
C | H : no evidence of correlation between runners’ positions, H : evidence of positive correlation between number of
0 1
failures and temperature [“evidence” does not belong in hypotheses; without “evidence of”2 this would be B1] | B0
D | H :  = 0, H :   0 [two errors: H wrong, no interpretation of ]
0 1 1 | B0
E | H :  = 0, H :   0 [two errors: H wrong, no interpretation of ]
0 1 1 | B0
F | H : r = 0, H : r > 0 [one error: no interpretation of . Allow use of r]
0 1 | B1
G | H :  = 0, there is no correlation between number of failures and temperature; H :  > 0, there is positive correlation
0 1
[two different answers, either of which would score 1 but neither gains 2 and we don’t give 1+1 here] | B1
H | H :  = 0, H :  > 0, where  is the pmcc [neither “population” nor context]
0 1 | B1
I | H :   0, H :  > 0, where  is the population pmcc
0 1
OR H :  = 0, H :  > 0, where  is the pmcc between temperature and number of failures
0 1 | B2
A | Reject H . There are more computer failures when temperatures are higher [too definite]
0 | M1A0
B | Reject H There is significant evidence of correlation [no context]
0. | M1A0
C | Sufficient evidence to reject H . There are more computer failures when temperatures are higher
0
[“Evidence” used, albeit in wrong sentence, but BOD] | M1A1
D | Wrong but validly obtained TS leading consistently to Do not reject H . There is insufficient evidence that there are
0
more computer failures when temperatures are higher [standard FT] | M1A1
E | Wrong but validly obtained TS leading consistently to Do not reject H There is evidence that the number of computer
0.
failures is not correlated with temperature. [Non-rejection doesn’t give positive evidence that H is correct. When H is
0 0
not rejected, candidates should aim for a “double negative”] | M1A0
F | (from correct TS and CV) Do not reject H . (+ anything) [inconsistent]
0 | M0A0
G | If H , H the wrong way round, but calculations right: Reject H . (+ anything)
0 1 0 | M1A0
Response | Mark
A | 12 is very high so it does cast doubt [relevant comparison needs to be seen] | B0B1
B | The probability is so low that 12 is worrying so it does cast doubt [unclear comparison] | B0B1
C | 0.0653 is not equal to 0.12 so probably not valid [don’t allow “not equal”] | B1
D | 0.0653 is not close to 0.12 | B1
E | 12 is much higher than 6.53 so it is not valid [too definite] | B1B0
F | P(= 12) from B(100, 0.0653) = 0.0166 which is very small so it does cast doubt | B0B1
G | P(> 12) from B(100, 0.0653) = 0.00784 which is very small so it does cast doubt | B0B1
H | P( 12) from B(100, 0.0653) = 0.00784 which is very small so it does cast doubt | B0B1
I | P( 12) from B(100, 0.0653) = 0.0299 which is small so it casts doubt [0.035 from N(6.53, 6.1036)] | B1B1
J | Expected number is 1000.0653 = 6.53 which is very different from 12 so it does cast doubt | B1B1
K | Wrong p, e.g.: 0.142 not far from 0.12 so it does not cast doubt (0.142 from Po( 6), 0.0267 from Po( 7) | B1B1ft
L | Likewise: Expected number is 14.2 which is not very close to 12 so it does cast doubt | B1B1ft
M | Likewise: P( 12) from B(100, 0.142) = 0.319 which is not too low so it does not cast doubt | B1B1ft
PMT
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