9231 P41 - Nov 2020 - Q4 - 8 marks
6830
Members of the Sprints athletics club have been taking part in an intense training scheme, aimed at reducing their times taken to run 400 m . For a random sample of 9 athletes from the club, the times taken, in seconds, before and after the training scheme are given in the following table.
Athlete | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) |
|---|---|---|---|---|---|---|---|---|---|
Time before | 48.8 | 48.2 | 50.3 | 49.6 | 49.4 | 48.9 | 47.6 | 50.3 | 48.4 |
Time after | 47.9 | 47.8 | 49.6 | 49.1 | 49.6 | 48.9 | 47.7 | 49.1 | 48.1 |
The organiser of the training scheme claims that on average an athlete's time will be reduced by at least 0.3 seconds.
Test at the 10\% significance level whether the organiser's claim is justified, stating any assumption that you make.
Solutions and mark schemes for 9231 are temporarily available to admins only.