Standard +0.8 This is a Further Maths statistics question requiring execution of a Wilcoxon signed-rank test with proper handling of ties (the 4.2 value), correct ranking procedure, critical value lookup for n=9 at ~1% significance, and contextual interpretation. While methodical, it demands careful procedural accuracy and understanding of non-parametric hypothesis testing beyond standard A-level content.
6. A zoologist knows that the median body length of adults in a species of fire-bellied toads is 4.2 cm . The zoologist thinks he has discovered a new subspecies of fire-bellied toads. If there is sufficient evidence to suggest the median body length differs from 4.2 cm , he will continue his studies to confirm whether he has discovered a new subspecies. Otherwise, he will abandon his studies on fire-bellied toads.
The lengths of 10 randomly selected adult toads from the group being investigated are given below.
$$\begin{array} { l l l l l l l l l l }
5 \cdot 0 & 3 \cdot 2 & 4 \cdot 9 & 4 \cdot 0 & 3 \cdot 3 & 4 \cdot 2 & 6 \cdot 1 & 4 \cdot 3 & 4 \cdot 8 & 5 \cdot 9
\end{array}$$
Carry out a suitable Wilcoxon signed rank test at a significance level as close to \(1 \%\) as possible and give your conclusion in context.
FT their differences provided M1M1 awarded. M1A0M1A0 if rank of 1 assigned to diff \(= 0\). FT \(n=10\) if M1A0M1A0 awarded
Upper CV \(= 43\) OR Lower CV \(= 2\)
B1
FT their TS and CV
Because \(30 < 43\) OR \(15 > 2\), there is insufficient evidence to reject \(H_0\)
B1
cso
The test suggests that the zoologist should abandon his studies on this population.
E1
## Question 6:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0$: median $= 4.2$, $H_1$: median $\neq 4.2$ | B1 | Both $H_0: \eta = 4.2$, $H_1: \eta \neq 4.2$ |
| Differences and ranks calculated correctly | M1, A1 | Condone mean differences |
| $W^+ = 5+4+9+1+3+8 = 30$ OR $W^- = 7+2+6 = 15$ | M1 | Attempt at summing ranks |
| $= 30$ OR $= 15$ | A1 | FT their differences provided M1M1 awarded. M1A0M1A0 if rank of 1 assigned to diff $= 0$. FT $n=10$ if M1A0M1A0 awarded |
| Upper CV $= 43$ OR Lower CV $= 2$ | B1 | FT their TS and CV |
| Because $30 < 43$ OR $15 > 2$, there is insufficient evidence to reject $H_0$ | B1 | cso |
| The test suggests that the zoologist should abandon his studies on this population. | E1 | |
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6. A zoologist knows that the median body length of adults in a species of fire-bellied toads is 4.2 cm . The zoologist thinks he has discovered a new subspecies of fire-bellied toads. If there is sufficient evidence to suggest the median body length differs from 4.2 cm , he will continue his studies to confirm whether he has discovered a new subspecies. Otherwise, he will abandon his studies on fire-bellied toads.
The lengths of 10 randomly selected adult toads from the group being investigated are given below.
$$\begin{array} { l l l l l l l l l l }
5 \cdot 0 & 3 \cdot 2 & 4 \cdot 9 & 4 \cdot 0 & 3 \cdot 3 & 4 \cdot 2 & 6 \cdot 1 & 4 \cdot 3 & 4 \cdot 8 & 5 \cdot 9
\end{array}$$
Carry out a suitable Wilcoxon signed rank test at a significance level as close to $1 \%$ as possible and give your conclusion in context.\\
\hfill \mbox{\textit{WJEC Further Unit 5 2022 Q6 [8]}}