2024 CJC P2 Q8

A giant panda’s daily diet consists almost entirely of leaves, stems and shoots of various bamboo species. A panda foundation claims that giant pandas consume on average at most \(25\) kg of bamboo every day to meet their energy needs. A random sample of \(40\) pandas is taken and the mass, \(x\) kilograms, of bamboo consumed per day by this group of pandas is summarised below.

\(\sum{\left( x-25 \right)=80.4}\), \(\sum{{{\left( x-25 \right)}^{2}}=1893.5}\)

1. Calculate the unbiased estimates of the population mean and variance for the mass of bamboo consumed per day by pandas.[2]
2. State the hypotheses that can be used to test whether the panda foundation’s claim is valid. By finding the \(p\)-value, carry out the test at \(2\%\) level of significance, giving your conclusion in the context of the question.[4]
3. State, in context, the meaning of the \(p\)-value found in part (b).[1]

Another random sample of \(n\) pandas is selected by zookeepers in a certain country and the sample mean was found to be \(26.9\) kg per day. A test was carried out at \(2\%\) level of significance.

4. By using the unbiased estimate of the population variance found in (a), find the least possible value of \(n\) such that this new sample achieves a different conclusion from that in (b).