Based on observations over a long period, the mean time taken by male students in Griffles Junior Co

Question

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: $$11, 11.5, 10.8, 11.2, 11.4, 11, 11.8, 12.5$$ Write down the null and alternative hypotheses for this test, defining any symbols you use.[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. 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]

Accepted Answer

(b)critical region : $(0,9.56]\cup[13.0,\infty)$ (c)$n\geq 90$, where $ n \in \mathbb{Z^+}$

2025 RI P2 Q9

2025 RI P2 Q9