Standard +0.3 This is a straightforward hypothesis test with given summary statistics. Students must calculate the sample mean (17085/300 = 56.95), recognize they need to find the sample standard deviation from the summaries, set up H₀: μ = 56.80 vs H₁: μ ≠ 56.80, compute the test statistic, and compare to critical values at 10% level. While it requires multiple steps and careful calculation, it follows a standard procedure with no conceptual challenges beyond routine A-level statistics—slightly easier than average due to being a textbook application.
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. [0pt]
[10] [0pt]
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.\\[0pt]
[10]\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Statistics 2026 Q7 [10]}}