Moderate -0.8 This is a straightforward hypothesis test for correlation requiring only standard steps: stating H₀ and H₁, comparing the test statistic |-0.45| = 0.45 to the given critical value 0.2787, and concluding. The critical value is provided, eliminating any need for tables or calculations. This is simpler than average A-level questions which typically require more calculation or conceptual work.
A medical student believes that, in adults, there is a **negative correlation** between the amount of nicotine in their blood stream and their energy level.
The student collected data from a random sample of 50 adults.
The correlation coefficient between the amount of nicotine in their blood stream and their energy level was \(-0.45\)
Carry out a hypothesis test at the 2.5% significance level to determine if this sample provides evidence to support the student's belief.
For \(n = 50\), the critical value for a one-tailed test at the 2.5% level for the population correlation coefficient is 0.2787
[4 marks]
Question 16:
16 | States
H : = 0
0
H : < 0
1 | 2.5 | B1 | H : = 0
0
H : < 0
1
–0.45 < –0.2787
Reject 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
Compares ± 0.45 or − 0 .4 5
and ±0.2787
May be seen on a diagram | 3.5a | M1
States –0.45 < –0.2787 or
0.45 > 0.2787 or
−0.45 > 0.2787 or
−0.45 > 0 .2 7 8 7
and
Infers H rejected
0
Condone accept H
1 | 2.2b | A1
Concludes, from a fully correct
comparison, in context by
referring to negative
correlation between the
amount of nicotine in the blood
stream and the energy level in
adults
Conclusion must not be definite,
eg use of ‘suggest’, ‘support’ etc
To be awarded R1, marks M1A1
must be scored as the minimum | 3.2a | R1
Question 16 Total | 4
Q | Marking instructions | AO | Marks | Typical solution
A medical student believes that, in adults, there is a **negative correlation** between the amount of nicotine in their blood stream and their energy level.
The student collected data from a random sample of 50 adults.
The correlation coefficient between the amount of nicotine in their blood stream and their energy level was $-0.45$
Carry out a hypothesis test at the 2.5% significance level to determine if this sample provides evidence to support the student's belief.
For $n = 50$, the critical value for a one-tailed test at the 2.5% level for the population correlation coefficient is 0.2787
[4 marks]
\hfill \mbox{\textit{AQA Paper 3 2024 Q16 [4]}}