| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2019 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Pearson’s product-moment correlation coefficient |
| Type | One-tailed test for positive correlation |
| Difficulty | Moderate -0.8 This is a straightforward hypothesis testing question requiring students to: (1) identify that a 1-tailed test is appropriate since the claim is directional ('greater'), (2) compare the calculated correlation coefficient (0.567) with the critical value (0.549) at 5% significance, and (3) state the conclusion. The critical values are provided in a table, eliminating any calculation. This is simpler than average A-level statistics questions as it tests only basic understanding of hypothesis testing with correlation coefficients. |
| Spec | 2.05g Hypothesis test using Pearson's r5.08d Hypothesis test: Pearson correlation |
| 1-tailed test significance level | 5\% | 2.5\% | 1\% | 0.5\% |
| 2-tailed test significance level | 10\% | 5\% | 2\% | 1\% |
| Critical value | 0.549 | 0.632 | 0.716 | 0.765 |
| Answer | Marks | Guidance |
|---|---|---|
| 15 | Identifies critical value = 0.549 | 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| critical value chosen from the table | 3.5a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| the table | 2.2b | R1F |
| Total | 3 | |
| Q | Marking Instructions | AO |
Question 15:
15 | Identifies critical value = 0.549 | 1.1b | B1 | 0.567 > 0.549
There is sufficient evidence
that the larger the rainfall, the
greater the yield.
Compares 0.567 correctly to their
critical value chosen from the table | 3.5a | M1
Makes correct inference
eg there is sufficient/significant
evidence that the larger the rainfall,
the greater the yield/positive
correlation between the two
FT their critical value chosen from
the table | 2.2b | R1F
Total | 3
Q | Marking Instructions | AO | Mark | Typical SolutionJamal, a farmer, claims that the larger the rainfall, the greater the yield of wheat from his farm.
He decides to investigate his claim, at the 5\% level of significance.
He measures the rainfall in centimetres and the yield in kilograms for a random sample of ten years.
He correctly calculates the product moment correlation coefficient between rainfall and yield for his sample to be 0.567
The table below shows the critical values for correlation coefficients for a sample size of 10 for different significance levels, for both 1- and 2-tailed tests.
\begin{tabular}{|l|c|c|c|c|}
\hline
1-tailed test significance level & 5\% & 2.5\% & 1\% & 0.5\% \\
\hline
2-tailed test significance level & 10\% & 5\% & 2\% & 1\% \\
\hline
Critical value & 0.549 & 0.632 & 0.716 & 0.765 \\
\hline
\end{tabular}
Determine what Jamal's conclusion to his investigation should be, justifying your answer.
[3 marks]
\hfill \mbox{\textit{AQA Paper 3 2019 Q15 [3]}}