October 2020 Paper 3 Q2

EdexcelCurrent spec7 marksIncludes hypothesis testingCorrelation & Regression Large Data Set

2. A random sample of 15 days is taken from the large data set for Perth in June and July 1987.

The scatter diagram in Figure 1 displays the values of two of the variables for these 15 days.

Figure 1: scatter diagram of 15 points, x-axis from 0 to 20 with a break near 0, y-axis unlabelled; the points lie between x = 11 and x = 19 and show y tending to decrease as x increases, with two points on y = 0 — Figure 1

(a) Describe the correlation. (1)

The variable on the \(x\)-axis is Daily Mean Temperature measured in °C.

(b) Using your knowledge of the large data set,

(i) suggest which variable is on the \(y\)-axis,

(ii) state the units that are used in the large data set for this variable. (2)

Stav believes that there is a correlation between Daily Total Sunshine and Daily Maximum Relative Humidity at Heathrow.

He calculates the product moment correlation coefficient between these two variables for a random sample of 30 days and obtains \(r = -0.377\)

your hypotheses
your critical value

(3)

On a random day at Heathrow the Daily Maximum Relative Humidity was 97%

(d) Comment on the number of hours of sunshine you would expect on that day, giving a reason for your answer. (1)

Scheme	Marks	AO
Negative	B1	1.2
	(1)

Mark scheme (b)

Scheme	Marks	AO
(i) Rainfall or Pressure	B1	2.2b
(ii) mm or hPa or Pascals or hectopascals or mb or millibars	B1ft	1.1b
	(2)

Notes

(b)(i) B1: for mentioning “rainfall” (allow “rain” or “precipitation”) or “pressure” (if more than 1 answer both must be correct)
NB the other quantitative variable for Perth is: Daily Mean Wind Speed and scores B0
[Not allowed “wind speed” since \(r = +0.15\) and in winter might expect wind to raise temp]

(ii) B1ft: for giving the correct units. If Daily Mean Wind Speed (kn) or knots
“Wind speed” and “knots” would score B0B1 but any other variable scores B0B0

Mark scheme (c)

Scheme	Marks	AO
\(\mathrm{H}_0 : \rho = 0 \qquad \mathrm{H}_1 : \rho \neq 0\)	B1	2.5
Critical value: \(-0.361(0)\)	M1	1.1b
\(r \lt -0.3610\) so significant result and there is evidence of a correlation between Daily Total Sunshine and Daily Maximum Relative Humidity	A1	2.2b
	(3)

Notes

B1: for both hypotheses correct in terms of \(\rho\)

M1: for the correct critical value compatible with their H₁: allow \(\pm 0.361(0)\)
If the hypotheses are 1-tail then allow cv of \(\pm 0.3061\)
e.g. Alternative hypothesis with \(r \lt \pm 0.377\) implies a one-tail test or H₀ and H₁ in words saying “H₀: there is no correlation, H₁: there is correlation” is two-tail
If there are no hypotheses (or they are nonsensical) assume 2-tail so M1 for \(\pm 0.361(0)\)

A1: for a correct conclusion in context based on comparing \(-0.377\) with their cv.
Condone incorrect inequality e.g. \(-0.3610 \lt -0.377\) as long as they reject H₀
Do not accept contradictory statements such as “accept H₀ so there is evidence of …”
Can say “support for Stav’s belief”(o.e.e.g. “claim”) or “evidence of a correlation between sunshine and humidity” condone “negative correlation” or comments such as “if humidity is high amount of sunshine will be low”

Mark scheme (d)

Scheme	Marks	AO
Humidity is high and there is evidence of correlation and \(r \lt 0\) So expect amount of sunshine to be lower than the average for Heathrow(oe)	B1	2.2b
	(1)
	(7 marks)

Notes

B1: for stating low amount of sunshine (o. e.) and some reference to \(r \lt 0\) or fog
Check for the following 2 features:
(i) low sunshine: allow \(\leqslant 5\) hrs (LDS mean for 2015 is 5.3, humidity 97% is 4.1, \(\geqslant 97\)% is 3.1)
(ii) negative correlation may be described in words e.g. “high humidity gives low sunshine” or fog (LDS says >95% humidity is foggy) so less sunshine