2023 CJC P2 Q10

Vesla, an electric vehicle (EV) car manufacturer claims that their EV cars have an average travelling distance of \(650\) km on a single charge. A car reviewer on the MeTube online video sharing platform wants to test if the EV car manufacturer overstated its claim.

The MeTube car reviewer buys a Vesla EV car to conduct his own test drives. He records the travelling distance on a single charge, \(x\) km, on \(50\) different days over a year. The travelling distance on a single charge, \(x\) km, is summarised below:

\(\sum{\left( x-650 \right)}=-34.39\) \(\sum{{{\left( x-650 \right)}^{2}}}=22769.98\)

1. Calculate unbiased estimates of the population mean and variance of the travelling distance of an EV car on a single charge.[2]
2. State hypotheses that the MeTube reviewer can use to test if Vesla has overstated its claim about travelling distance on a single charge, defining any symbols you use. Work out the test statistic in this case, and use it to carry out the test at the \(5\%\) level of significance, giving your conclusion in the context of the question.[5]
3. Explain if the MeTube car reviewer needs to apply Central Limit Theorem for the test to be valid.[2]

Another car reviewer on the TokTik online video sharing platform wants to test if the EV car manufacturer’s claim is true. He rents a Vesla EV car to conduct his test drives where he records the travelling distance on a single charge. He records a random sample of \(6\) test drives and calculates the mean travelling distance on a single charge.

4. Explain whether the TokTik car reviewer should use a \(1\)-tail or a \(2\)-tail test.[1]
5. State two assumptions that allow the TokTik car reviewer to carry out his test.[2]