7. A machine is designed to make paper with mean thickness 56.80 micrometres. The thicknesses, \(x\) micrometres, of a random sample of 300 sheets are summarised by $$n = 300 , \quad \Sigma x = 17085.0 , \quad \Sigma x ^ { 2 } = 973847.0 .$$ Test, at the \(10 \%\) significance level, whether the machine is producing paper of the designed thickness.
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