June 2024 Paper 3 Q16
16 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]
| Scheme | Marks | AO |
|---|---|---|
| States \(\mathrm{H_0} : \rho = 0\) \(\mathrm{H_1} : \rho \lt 0\) | B1 | 2.5 |
| Compares ±0.45 or \(\lvert -0.45 \rvert\) and ±0.2787 May be seen on a diagram | M1 | 3.5a |
| States \(-0.45 \lt -0.2787\) or \(0.45 \gt 0.2787\) or \(\lvert -0.45 \rvert \gt 0.2787\) or \(\lvert -0.45 \rvert \gt \lvert 0.2787 \rvert\) and Infers \(\mathrm{H_0}\) rejected Condone accept \(\mathrm{H_1}\) | A1 | 2.2b |
| 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 | R1 | 3.2a |
| (4 marks) |
Typical solution
\[\mathrm{H_0} : \rho = 0\]\[\mathrm{H_1} : \rho \lt 0\]\[-0.45 \lt -0.2787\]Reject \(\mathrm{H_0}\)
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