Meaning of level of significance and its relation to p-value

Meaning of level of significance and its relation to p-value

A manufacturer claims that his device, a new product, when attached to the engine of cars, can help to improve the rate of fuel consumption. To test his claim, 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 \(17.8\) 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 \(5\%\) level of significance and it is found that there is a decrease in the rate of fuel consumption.

  1. State what you understand by the expression at \(5\%\) significance level in the context of the question.
  2. Find the smallest level of significance at which the test will indicate that there is a decrease in the rate of fuel consumption.

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Answer:(ii) \(\begin{align} & {{H}_{0}}:\mu =17.8 \\ & {{H}_{1}}:\mu <17.8 \\ \end{align}\), \(\alpha >8.29\)

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