June 2025 Paper 3 Q4

EdexcelCurrent spec9 marksIncludes hypothesis testingIncludes samplingCorrelation & Regression Data Processing Large Data Set

4. Kay is studying the variables Daily Total Sunshine (\(x\)) and Daily Total Rainfall (\(y\)) from the large data set for Leeming in 2015

Kay starts with 5th May and then selects every 10th day thereafter.

(a) State the name of the sampling technique Kay uses. (1)

Kay wants to find the regression line of \(y\) on \(x\) for these data.

(b) Using your knowledge of the large data set, explain how Kay might need to clean these data before finding the equation of the regression line. (1)

The equation of the regression line Kay finds is \(y = 0.741 + 0.199x\)

(i) state the units of the gradient of the regression line,

(ii) give an interpretation of the \(y\)-intercept of the regression line. (2)

Kay’s teacher claimed that the greater the amount of sunshine in a day the lower the amount of rain there should be.

(d) State, giving a reason, whether the teacher’s claim is true for Kay’s data. (1)

The teacher used all the data for these variables from the large data set for Leeming in 2015, as a sample.
The teacher calculated the product moment correlation coefficient for \(x\) and \(y\) to be \(-0.160\)

In a suitable test to determine whether there is evidence to support the teacher’s claim, the \(p\)-value was 0.015

(e) Using a 5% level of significance, state the hypotheses and conclusion for this test. (2)

(f) For the test in part (e) describe

(i) the sample,

(ii) a possible population. (2)

Mark scheme (a)

Scheme	Marks	AO
Systematic (sampling)	B1	1.2
	(1)

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.

Mark scheme (b)

Scheme	Marks	AO
The (Daily Total) Rainfall data may contain “tr” entries (these will need a suitable value substituted before calculations can take place.)	B1	2.4
	(1)

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.

Mark scheme (c)

Scheme	Marks	AO
(i) mm/h (o.e.) e.g. \(\mathrm{mm\,h^{-1}}\) or \(\mathrm{mm\,hrs^{-1}}\) or \(\dfrac{\text{mm}}{\text{hours}}\)	B1	1.1b
(ii) When there is no sun(shine) there is (on average) 0.7(41) (mm) of rain or the amount of rain when there is no sun(shine) (o.e.)	B1	2.4
	(2)

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)

Mark scheme (d)

Scheme	Marks	AO
e.g. Not consistent (since); Kay’s line says positive correlation or gradient or regression coefficient or regression line or 0.199 is positive	B1	2.4
	(1)

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

Mark scheme (e)

Scheme	Marks	AO
\(\mathrm{H}_0 : \rho = 0\) and \(\mathrm{H}_1 : \rho < 0\)	B1	2.5
[\(p\)-value < 5% so significant result] there is evidence to support the teacher’s claim	B1	2.2b
	(2)

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 \(0.015 < 0.05\)]

Mark scheme (f)

Scheme	Marks	AO
(i) The sample is rainfall (\(y\)) and sunshine (\(x\)) for May~Oct in (Leeming) in 2015	B1	1.1b
(ii) e.g. (rainfall and sunshine) for: (Leeming) for all of 2015, or Leeming anytime (not just May~Oct) or Leeming for May~October for other years too or May~Oct in UK etc	B1	3.3
	(2)
	(9 marks)

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.