Edexcel A-Level Mathematics A2 S3.2 Sampling Questions

Randomly select a student from 1 to 7 oe
Take every $7{ }^{\text {th }}$ student
(2)

B1 B1

To generate a simple random sample, Luka would need to generate two-digit numbers (from 00 to 69)

B1

But Luka's table would not be suitable for generating random two-digit
numbers

B1 B1ft

Stratified sampling reflects the population structure.
Marking guidance for this part:
B1 for any correct advantage, for example that it allows calculations of statistics for each city or group.

\multirow{4{*}{Kettle & A & B & C & D & E & F & G

Price (£) & 99.99 & 14.99 & 34.97 & 49.99 & 19.97 & 29.99 & 8.99

Aarush Rank & 2 & 5 & 4 & 1 & 7 & 3 & 6

Actual rank & 1 & 6 & 3 & 2 & 5 & 4 & 7
\end{tabular}}}

$\sum d^{2}=1+1+1+1+4+1+1\ [=10]$}
$r_s=1-\frac{6\times10}{7\times48}$}
$=0.8214 \ldots$

awrt 0.821

A1cso

(4)

$\mathrm{H}_{0}:\rho=0\quad\mathrm{H}_{1}:\rho>0$}
Critical Value $r_{s}=0.7143$}
Either reject $\mathrm{H}_{0}$ result is significant/ $r_{s}$ does lie in the critical region}
Conclude there is evidence to support that Aarush can rank the
kettles in order of price.
(4)

Aarush has already ranked them or the order / price is not normally
distributed
(1)

(d)

Kettle A and D would have a tied rank (1.5)
(1)

Notes

Total 10

(a)

M1 for an attempt to rank Aarush's order and actual order ( at least 4 correct in either row)

M1 for finding differences between each pair of their ranks and evaluating $\sum d^{2}$ imp by A1}

dM1 dependent on previous 2 M marks being awarded. Using $r_{s}=1-\frac{6\sum d^{2}}{7\times48}$}

A1 awrt 0.821 or allow $\frac{23}{28}$}

(b)

B1 both hypotheses stated in terms of $\rho$ or $\rho_{s}$ (condone if appears as p- it cannot be in
terms of r ) If their $r_{\mathrm{s}}<0$ condone $\mathrm{H}_{1}: \rho<0$}

M1 allow $\mid$ their $\mathrm{CV}=0.7143$ or better}

M1 for a correct non-contradictory statement consistent with their $r_{s}\left(r_{s}<1\right)$ and their CV
if signs are compatible. Allow eg Accept $\mathrm{H}_{1}$ or for correct conclusion in context on its own.}

A1 dependent on all of the previous method marks but independent of hypotheses. For
correct conclusion in context which must be rejecting $\mathrm{H}_{0}$ and has rank, kettles and price
and no contradictory statements.}

(c)

B1 for a correct reason e.g. (some of) the data has already been ranked, Aarush has not
given the prices (only the ranks) oe. Condone "it is ordinal data"

(d)

B1 for the idea that both A and D will have same rank (1.5) If the rank is stated it must be 1.5. Must mention both A and D (or imply) and allow explanations such as "equal rank", "average rank". Condone "order" for rank.

If an incorrect rank or letter pairing is given then B0.

Question
Number

Scheme

Marks