Pure Mathematics
Statistics

Worked Example 5

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

[latex]\sum{x=110200}[/latex] and [latex]\sum{{{x}^{2}}}=180512000[/latex]

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

(i)

State what you understand by the expression at the [latex]8\%[/latex] significance level in the context of the question.

(ii)

Find the range of the level of significance at which the test will indicate that the population mean lifetime is not [latex]1500[/latex] hours.

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