Notes

B1: for systematic (ignore other non-contradictory descriptions). Condone misspelling.
If a clear choice is given e.g. stratified or systematic we take the final answer.

Notes

B1: for mention of “tr” or “trace” entries in rain(fall) [ or \(y\)] data. Ignore “n/a”.
Ignore any comment about what to do with trace.

Notes

(i) B1: for mm/h or equivalent in words.

(ii) B1: for the idea of amount of rain when no sun. “Minimum rain” is B0
Don’t need value or units but if given must be correct or consistent with (i)

Notes

B1: for a suitable reason and saying not consistent (o.e.) e.g. “false” or “untrue” or “no”
Reason only needs to be about the line and may be a description e.g. as \(x\) increases \(y\) increases or at least 2 values of \(x\) substituted and \(y\) values evaluated

Notes

B1: for both hypotheses correct in terms of \(\rho\) (condone attempt at \(\rho\) that looks like \(p\))

B1: for a correct conclusion in context with no contradiction.
Using words “support” and “teacher’s claim”
or “negative correlation” and “sun or \(x\)” and “rain or \(y\)”
[If a comparison is given it must be \(0.015 < 0.05\)]

Notes

(i) B1: for recognising that all the data/days for these variables in LDS for 2015 is the sample.
Condone omitting “Leeming”
B0 for “sunshine and rainfall for Leeming in 2015” It could be the population.

(ii) B1: for a suitable attempt to describe a population. The teacher’s sample must be a subset.

Notes

B1 for a suitable interpretation in context [value can be 1.3 or 1.28 or “just over 1”] per sec
Must have underlined words (o.e.) and units “m” or metres and “s” or seconds
NB “descends” implies “height decreases”
Condone e.g. “decreases by \(-\,1.28\) m”

Notes

B1 for both hypotheses correct in terms of \(\rho\) [accept a \(p\) or p but not \(r\) or r]
Must be attached to \(\mathrm{H_0}\) and \(\mathrm{H_1}\)

M1 for a critical value corresponding to their \(\mathrm{H_1}\):
1-tail: awrt \(\pm\,0.549\) or 2-tail (B0 scored for \(\mathrm{H_1}\)): awrt \(\pm\,0.632\) (tables 0.6319)
If hypotheses are in words and can deduce whether one or two-tail then use their words.
If no hypotheses or their \(\mathrm{H_1}\) is not clearly one or two-tail assume one-tail

A1 a correct conclusion in context mentioning correlation and height and time
A comparison or statement such as “not sig” is not needed but if seen must be correct.
Do NOT award this A mark if contradictory comments or working seen e.g. “reject \(\mathrm{H_0}\)” or comparison of 0.510 with significance level of 0.05 or e.g. \(-0.549 \gt -0.510\)

NB Can award B0M1A1

SC B0(for 2-tail) M0(for cv = \(\pm\,0.549\)) scored: Allow 1 mark (score as B0M0A1) for conclusion such as: “insufficient evidence of (negative) correlation between height and time of flight”

Notes

B1 for saying no and giving a suitable supporting reason
Don’t allow “correlation” on its own instead of “gradient”
B0 for simply saying “points don’t lie close to a straight line” Need mention of curve or some other feature of scatter plot that differs from regression line.
B0 for just “non-linear” without mention of the model being linear
B0 for simply comparing 1 or 2 points – need a comment about general pattern

Notes

B1 for a value of \(k\) in the range [3, 4.5]   Do not need \(k = \ldots\)
Accept a value embedded in Jane’s model. ISW any errors in multiplying out bracket.

Typical solution

Typical solution

Reject \(\mathrm{H_0}\)

There is sufficient evidence to suggest the student’s belief that, in adults, there is a negative correlation between the amount of nicotine in their blood stream and their energy level

Typical solution

Notes

B1 B1: Subtract B1 for each error:

• Undefined \(\rho\): B1B0
• 1-tail: B1B0
• Allow other letters (but not \(r\), \(c\) or \(h\): B1B0)
• Hypotheses in words (no parameter): B1B0
  • \(\mathrm{H}_0\): There is no correlation
  • \(\mathrm{H}_1\): There is correlation
  • Do not allow “negative” or “positive” correlation for \(\mathrm{H}_1\): B0B0

Accept “pmcc” for correlation coefficient

B1FT: FT their setup/hypotheses

• e.g. for \(\mathrm{H}_1: \rho \lt 0\), compare 0.798 with 0.6581

Must use \(n = 12\) and specify a corresponding value from the table

• 0.6581 or 0.7079 only (NB not 0.6851 from \(n = 11\))

Must compare this with 0.798 with the same sign

• Condone \(-0.798 \lt -0.7079\) or \(|-0.798|\)
• Do not accept \(-0.798 \lt 0.6581\)

NB this is the only mark that can be scored with no hypotheses

M1: This step must be seen, consistent with their hypotheses and their comparison. Condone Accept \(\mathrm{H}_1\)

A1: Conclusion must be in context, not definite and consistent with their hypotheses and comparison.

• Disregard any mention of “negative” or “positive”
• “Relationship” A0
• “Prove(d)” A0
• Condone “there is evidence of a linear correlation between \(h\) and \(c\)”
• Condone “significant” for “sufficient”

Must conclude that there is evidence for a correlation.

Notes

B1: For a statement about the relative strength of the linear correlation:

• Accept “points form a line” or
• Accept “points lie (relatively) close to the line”
• Not “points are close together” or “close to each other”

B1: For a statement about the appearance of the negative correlation:

• Accept “line from 2^nd to 4^th quadrant”
• Accept “two clusters in top left and bottom right”
• Accept “line will be downwards sloping”
• Not “negatively correlated” (must be a feature of the scatter diagram)

This mark only may be implied by a sketch (showing a scatter diagram with negative correlation, with or without a line of best fit).

Notes

B1: oe, may be implied (but do not allow “independent”)

B1: Any sensible comment about the statement but must be in context:

• Accept “Some people may not visit if the store is too cold”
• Accept “the shop being too warm may mean customers don’t want to go inside”
• Not “There may be a third factor affecting both \(c\) and \(h\)” (a possible factor must be specified)
• Accept “more people in the store may mean there is less need for heating” (so the implication might be the other way around) or equivalent statements about causation

Notes

B1: For the setup, condone “n=10” but must reference ‘no correlation’

B1: Allow \(\geqslant\)
Accept an equivalent statement in words, but it must be about a probability:

• e.g. “The probability that the pmcc is greater than 0.7155 is 1%”
• e.g. “There is a 1% chance that there is actually no correlation when \(r\) is greater than 0.7155.”

Notes

Or eg "Expect weight to increase with time" oe
"Foetuses grow" oe
Ignore all else

Notes

B1B0 for 1 error, eg undefined \(\rho\) or 2-tail

For hypotheses in words, not using parameter:
\(\mathrm{H}_0\): There is no correlation between time and weight
\(\mathrm{H}_1\): There is positive correlation between time and weight B1B0
But omission of “positive”: B0B0

M1: May be implied by conclusion

A1: Allow without "positive” and without “linear"
In context, not definite

Notes

(i) B1: allow convenience (sampling)
do not allow eg convenient sampling; eg opportunistic sampling

(ii) B1: allow so
any eg which alludes to sample possibly giving unrepresentative values

Notes

B1: ignore adjectives such as weak, strong etc
allow
eg as mean hours spent running increases, resting pulse rate decreases;
eg negative relationship;
do not allow
eg (negative) correlation;
eg as pulse rate increases, mean hours per week spent running decreases

Notes

B1: approximately vertical line at about 2.5; B0 if more than one line

Notes

B1: allow eg \(r_s\) is closer to 0 than to 1;
eg low value of \(r_s\); eg allow \(r_s\) close to 0

M1: allow eg \(p\)-value \(\gt\) 0.05 (or 0.01 or 0.1)
eg \(p\)-value not small
do not allow
eg \(p\)-value (relatively) large
eg high \(p\)-value

A1: may infer no association

B1: allow
eg \(r_s\) close to \(-1\)
eg \(r_s\) is closer to –1 than 0;
eg \(r_s\) is not small
B0 for eg \(r_s\) is large oe

M1: allow eg \(p\)-value \(\lt\) 0.05 (or 0.01 or 0.10)
allow eg \(p\)-value is (very) small/low

A1: may infer negative association

Notes

B1: allow eg as cost of electricity increases, cost of gas increases oe

Notes

M1: allow eg “\(p\)-value \(\gt 0.05\)”

A1: allow \(p\)-value \(\gt 0.025\)

A1: A0 if refers to correlation rather than association; dependent on award of previous A1

Notes

B1: LDS advantage
do not allow if answer spoiled
eg because it’s an anomaly,
eg because it’s an outlier,

Notes

B1: ignore extra comments unless they contradict an otherwise correct answer

B1: ignore extra comments unless they contradict an otherwise correct answer

Notes

M1: use of 2 standard deviation check for one of the 4 calculations soi

A1: allow \(\leqslant\) and \(\geqslant\)

A1: allow \(\leqslant\) and \(\geqslant\)

if M1A0A0 allow M1 SCB1 for all 4 correct values seen

Notes

B1: need to refer to the shape of the scatter oe

Notes

B1: allow eg the first estimate..

B1: allow eg the second estimate…

Notes

B1: LDS advantage

Notes

B1: LDS advantage

B1: LDS advantage

Notes

B1: Point at (700, 47.56) ringed
LDS advantage

Notes

B1: must give specific range of values ; must say supports statement oe

B1: the range may be implied by reference to a specific range identified for the first mark; must say does not support statement oe

Notes

B1: allow he should have compared \(r\) with the critical value

if B0B0 SC1 for Lee has confused \(r\) with \(p\) or for 0.37154 suggests positive correlation

Notes

M1: condone use of 201236 instead of 204356;
ignore work relating to lower tail
or \(521000 + 1.5 \times (521000 - 342500)\)

A1: numerical values must be mentioned
or 788750 in which case accept two or three outliers identified extra one is approximately 800 000
(corrected from the printed mark scheme: “867940 from use of 210236” is printed; 867940 comes from 201236)

Notes

if B0B0 allow SC1 for \(r\) closer to 0 and \(p\)-value larger

Notes

B1: gradient

B1: intercept

allow both marks for correct equation in any form isw
allow eg \(y = 28\,500x - 57\,184\,000\)

Notes

FT their straight line model provided this gives values > 250 000

Notes

B1: dependent on correct values in (b)

B1: FT comment for their values > 250 000
this mark is dependent on having calculated values in part (d)