Deducing of Inequalities Using Classical Hypothesis Testing

A manufacturer invented a new device to be attached to the engine of cars. A test is to be carried out to investigate the effect of the device on the rate of fuel consumption of cars. The device was attached to the engines of \(100\) cars of a particular model whose rate of fuel consumption is known to have a mean of \(\mu_{0}\) km per litre. The results are summarised as follows:

\(\sum (x-16)=173.4\) and \(\sum (x-16)^{2}=323.12\)

A statistical test is carried out at \(8\%\) level of significance and it is found that the device has no impact on the rate of fuel consumption.

Find the range of values of \(\mu_{0}\).