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Exam-Style Question on StatisticsA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 604. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is allowed.
Miss Chloe Sharpe (singing teacher) was teaching nine students last year. At the end of the year the students took a singing exam and their results were reported as percentages. Chloe decided to record the average number of hours per week each student reported practising in the weeks before the examination.
These results can be seen in the table below.
| Average weekly practice time (\(p\)) | 25 | 30 | 23 | 28 | 34 | 27 | 36 | 19 | 28 |
|---|---|---|---|---|---|---|---|---|---|
| Percentage score (\(s\)) | 70 | 89 | 64 | 88 | 97 | 81 | 95 | 70 | 85 |
(a) Find Pearson's product-moment correlation coefficient, \(r\), for these data.
(b) The relationship between the variables can be modelled by the regression equation \(s = ap + b\). Write down the value of \(a\) and the value of \(b\).
(c) One of these nine students was disappointed with his result and wished he had practised more. Based on the given data, determine how his score could have been expected to alter had he practised an extra four hours per week.
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