9231 P41 - Nov 2021 - Q4 - 8 marks
6806
Manet has developed a new training course to help athletes improve their time taken to run 800 m . Manet claims that his course will decrease an athlete's time by more than 2 s on average. For a random sample of 10 athletes the times taken, in seconds, before and after the course are given in the following table.
Athlete | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) |
|---|---|---|---|---|---|---|---|---|---|---|
Before | 150 | 146 | 131 | 135 | 126 | 142 | 130 | 129 | 137 | 134 |
After | 145 | 138 | 129 | 135 | 122 | 135 | 132 | 128 | 127 | 137 |
Use a \(t\)-test, at the \(5 \%\) significance level, to test whether Manet's claim is justified, stating any assumption that you make.
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