Pure Mathematics
Statistics

Worked Example 6

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 [latex]100[/latex] EVs of a particular model whose driving range is known to have a mean of [latex]{{\mu }_{0}}[/latex] km per charge. The driving range, [latex]x[/latex] km, of each EV was recorded and the following data are obtained:

[latex]\sum{\left( x-240 \right)=800}[/latex] and [latex]\sum{{{\left( x-240 \right)}^{2}}=10240}[/latex]

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

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