2007 TPJC P2 Q8

The rate of fuel consumption of a brand of car called Missan is known to have a mean of \(m\) km per litre. A new device has been introduced in the manufacturing process to improve the car’s fuel consumption rate. A sample of \(100\) ‘improved’ cars selected gave the following data:

\(\sum{\left( x-17 \right)}=180\) and \({{\sum{\left( x-17 \right)}}^{2}}=2550\)

1. A statistical test is carried out at \(5\%\) significance level and it is found that the device has been effective. Find the range of values of \(m\).[6]
2. State what you understand by the expression ‘at \(5\%\) significance level’ in the context of this question.[1]