A2 June 2023 Q5

EdexcelCurrent spec9 marksIncludes hypothesis testingt-Tests & Further Tests

5. A psychologist claims to have developed a technique to improve a person’s memory.

A random sample of 8 people are each given the same list of words to memorise and recall.

Each person then receives memory training from the psychologist. After the training, each person is given the same list of new words to memorise and recall.

The table shows the percentage of words recalled by each person before and after the training.

Person	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)
Percentage of words recalled before training	24	33	33	39	30	38	32	34
Percentage of words recalled after training	28	30	37	41	32	44	35	34

(a) State why a paired \(t\)-test is suitable for these data. (1)

(b) State an assumption that needs to be made in order to carry out a paired \(t\)-test in this case. (1)

(c) Test, at the 5% level of significance, whether or not there is evidence of an increase in the percentage of words recalled after receiving the psychologist’s training.
State your hypotheses, test statistic and critical value used for this test. (7)

Scheme	Marks	AO
e.g. for each person the scores before and after are not independent	B1	2.4
	(1)

Scheme	Marks	AO
The differences in scores are normally distributed.	B1	2.4
	(1)

Mark scheme (c)

Scheme	Marks	AO
\(d\): \(4\quad -3\quad 4\quad 2\quad 2\quad 6\quad 3\quad 0\)	M1	3.1b
\(\bar{d} = \pm 2.25 \qquad s_d = \sqrt{7.642857\ldots} = 2.76457\ldots\)	M1	1.1b
\(\mathrm{H}_0 : \mu_\mathrm{d} = 0 \qquad \mathrm{H}_1 : \mu_\mathrm{d} \gt 0\)	B1	3.3
\(t = \pm\dfrac{\text{“}\pm 2.25\text{”}}{\frac{\text{“}2.76\ldots\text{”}}{\sqrt{8}}}\)	M1	1.1b
\(= \pm 2.3019\ldots\) awrt \(\boldsymbol{\pm 2.30}\)	A1	1.1b
Critical value \(t_7 = \pm 1.895\)	B1	1.1b
2.30 > 1.895, therefore (reject H₀) there is sufficient evidence to: support an increase in the percentage of words recalled or support psychologist’s claim	A1ft	2.2b
	(7)
	(9 marks)

Notes

M1: for setting up paired \(t\)-test with at least 5 correct differences consistent in direction

M1: complete method for \(\bar{d}\) and \(s_\mathrm{d}\) or \(s_d^{\,2}\)

B1: Use of \(t\)-distribution for differences with both hypotheses correct in terms of \(\mu\) / \(\mu_\mathrm{d}\)
Allow \(\mu_\mathrm{d} \lt 0\) if candidate does test with negative test statistic

M1: method for finding test statistic with their values

A1: awrt \(\pm\)2.30

B1: correct critical \(\pm\)1.895 (or better) with compatible sign

A1ft: drawing a correct inference in context
Must be consistent with their CV and a standardised test statistic from \(t\)-distribution
Must mention “percentage” and “words” or “psychologist’s claim”

SC: If they have carried out a \(t\)-test for two independent samples they can potentially score: M0M0B0M1A0B1A1ft
If they do follow this path, they can score:
3^rd M1 for standardising with difference of their means and a pooled variance
2^nd B1 for a CV of 1.761
A1ft for a correct contextual conclusion for their test statistic and 1.761