Worked Example 5

A sample of \(80\) light bulbs is taken from a population with a mean lifetime of \(1500\) hours. The lifetime, \(x\) hours, of each lightbulb was recorded and the following data are obtained:

\(\sum{x=110200}\) and \(\sum{{{x}^{2}}}=180512000\)

A statistical test is carried out at a \(8\%\) level of significance, and it is found that the population mean lifetime is not \(1500\) hours.

1. State what you understand by the expression at the \(8\%\) significance level in the context of the question.
2. Find the range of the level of significance at which the test will indicate that the population mean lifetime is not \(1500\) hours.