2025 RI P2 Q9

Based on observations over a long period, the mean time taken by male students in Griffles Junior College (GJC) to complete a \(2.4\) km run is known to be \(11.3\) minutes with a standard deviation of \(2.2\) minutes. As part of a review of the current physical training programme, the Physical Education (PE) department in GJC decided to test, at the \(2.5\%\) level of significance, whether the mean time taken by male students in GJC to complete a \(2.4\) km run has changed. The time taken, \(x\) minutes, by a random sample of \(8\) Year \(5\) male students from GJC to complete a \(2.4\) km run, are as follows:

\({11 \quad 11.5 \quad 10.8 \quad 11.2 \quad 11.4 \quad 11 \quad 11.8 \quad 12.5}\)

1. Write down the null and alternative hypotheses for this test, defining any symbols you use.[2]
2. Stating a necessary assumption, find the critical region for this test. Hence state the conclusion of the test in the context of the question.[6]

The PE department in GJC also conducted a second test, at the \(3\%\) level of significance, to determine whether the mean time taken by female students in GJC to complete a \(2.4\) km run is less than \(14.5\) minutes. A random sample of \(n\) female students from GJC is taken, where \(n\) is large. The mean and standard deviation of the time taken by this sample to complete a \(2.4\) km run are found to be \(14.2\) minutes and \(1.5\) minutes respectively.

3. Given that the PE department concludes that the mean time taken by female students to complete a \(2.4\) km run is less than \(14.5\) minutes, find the range of values that \(n\) can take.[5]