CAIE A-Level Further Math A2 4.4.4 Paired Non Parametric Tests Questions

5 & 7 & -6 & 1 & -4 & 2 & 8 & 26 & -10

4 & 6 & -5 & 1 & -3 & 2 & 7 & 9 & -8
Differences, allow at most 2 errors.
Correct rank order, ignore signs.

[ P=29 ] Q=16
Condone P not excluded.

$\mathrm{H}_{0}$: population medians equal or $m_{1}=m_{2}$$\mathrm{H}_{1}$: population median X> population median Y or $m_{1}>m_{2}$
'Population' required. Accept use of m, not $\mu$.

Do not accept 'difference between population medians >0 ' without X, Y OE specified.

Critical value =8
16>8 and accept $\mathrm{H}_{\mathrm{o}}$ / not significant
Compare their ' 16 ' with their ' 8 ' and conclusion.
Their '16' must be less than 23. Ignore their hypotheses.
Condone 'reject $\mathrm{H}_{1}$ '.

Insufficient evidence to support teacher's belief
or
insufficient evidence that the marks/median in Paper 1 are/is
higher than the marks/median in Paper 2
Correct conclusion in context, following correct work, level of
uncertainty in language (not 'prove', not 'there is no evidence'),
no contradictions.
e.g. Proves that the teacher is incorrect scores A0. A0 if
hypotheses wrong way round.

7