Deducing of Inequalities Using Classical Hypothesis Testing

A manufacturer claims that his new battery management system, when installed in electric vehicles (EVs), can help to improve the driving range. To test his claim, the system was installed in \(100\) EVs of a particular model whose driving range is known to have a mean of \(\mu_{0}\) km per charge. The driving range, \(x\) km, of each EV was recorded and the following data are obtained:

\(\sum (x-240)=800\) and \(\sum (x-240)^{2}=10240\)

A statistical test is carried out at a \(5\%\) level of significance, and it is found that there is an increase in the driving range. Find the range of values of \(\mu_0\).