Moderate -0.8 This is a straightforward hypothesis test for correlation following a standard template: state hypotheses (H₀: ρ=0, H₁: ρ>0), compare the given r=0.379 with the critical value 0.4622, and conclude. It requires only recall of the hypothesis testing procedure with no calculations or conceptual challenges, making it easier than average.
An educational expert found that the correlation coefficient between the hours of revision and the scores achieved by 25 students in their A-level exams was 0.379
Her data came from a bivariate normal distribution.
Carry out a hypothesis test at the 1\% significance level to determine if there is a positive correlation between the hours of revision and the scores achieved by students in their A-level exams.
The critical value of the correlation coefficient is 0.4622
[4 marks]
Question 16:
16 | States both hypotheses
correctly for one-tailed test
Do not accept r = 0 and r > 0
Accept ρ in words eg.
:No correlation/coefficient is 0
:Positive
c𝐻𝐻o 0 rrelation/coefficient > 0
𝐻𝐻1 | 2.5 | B1 | : ρ = 0
: ρ > 0
𝐻𝐻0
𝐻𝐻0. 1 379 < 0.4622
Accept
There is𝐻𝐻 i 0 nsufficient evidence to
suggest that there is a positive
correlation between the hours of
revision and the scores achieved
by them in their A level exams
Compares given critical value
0.4622 with the given correlation
0.379 coefficient
Condone 0.462 or 0.46 or 0.5
for 0.4622
Condone 0.38 or 0.4 for 0.379 | 3.5a | M1
Compares given critical value
0.4622 with the given correlation
0.379 coefficient correctly and
infers is not rejected
Allow reference to
𝐻𝐻0 | 2.2b | A1
Concludes correctl y𝐻𝐻 i 1 n context
that there is insufficient
evidence to suggest that there
is positive correlation between
the hours of revision and the
scores achieved by them in
their A level exams | 3.2a | R1
Total | 4
Q | Marking Instructions | AO | Marks | Typical Solution
An educational expert found that the correlation coefficient between the hours of revision and the scores achieved by 25 students in their A-level exams was 0.379
Her data came from a bivariate normal distribution.
Carry out a hypothesis test at the 1\% significance level to determine if there is a positive correlation between the hours of revision and the scores achieved by students in their A-level exams.
The critical value of the correlation coefficient is 0.4622
[4 marks]
\hfill \mbox{\textit{AQA Paper 3 2020 Q16 [4]}}