|
|
Exam-Style Question on CorrelationA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 689. This question is similar to one that appeared on a GCSE Higher paper in 2022. The use of a calculator is allowed.
In the Bubbleless Bandits free-diving club, members practice breath-holding techniques as part of their routine.
In this club, the older members have been practicing these techniques for many years, leading to increased breath-holding capacity through disciplined training and improved technique. The older members tend to be the more experienced free-divers. They have mastered relaxation and breath control, contributing to their ability to hold their breath for longer periods.
The times, \( t \) seconds, that club members could hold their breath while diving and their ages, \( x \) years, are recorded. The results are shown in the table.
| Age, \( x \) years | Time, \( t \) seconds |
|---|---|
| 19 | 37 |
| 31 | 44 |
| 55 | 101 |
| 33 | 63 |
| 29 | 55 |
| 61 | 110 |
| 40 | 78 |
| 35 | 71 |
(a) Draw a scatter diagram to represent this data.
(b) What type of correlation is shown on the scatter diagram?
(c) Find the equation of the regression line giving your answer in the form \( t = ax + b \).
(d) Use your regression equation to estimate the time a person aged 45 could hold their breath.
(e) Give a reason why you should not use the regression equation to estimate the time it would take a person aged 14 to do the task.
|
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription. Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves. This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures. A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience. |
|
Drag this panel down to reveal the solution
If you need more practice try the self-checking interactive exercises called Estimating Correlation.
The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
The solutions to the questions on this website are only available to those who have a Transum Subscription.
Exam-Style Questions Main Page
To search the entire Transum website use the search box in the grey area below.
Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
©1997 - 2024 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/
