A machine is designed to make paper with mean thickness $56.8$ micrometres. The thickness, $T$ m

Question

A machine is designed to make paper with mean thickness $56.8$ micrometres. The thickness, $T$ micrometres, of a piece of paper made by the machine is normally distributed with standard deviation $2.85$ micrometres. A random sample of $300$ pieces of the paper is taken and a test is carried out, at the $5\%$ significance level, to determine whether the machine is producing paper of the desired thickness.

State appropriate hypotheses for the test.[1]

The sample mean thickness is denoted by $\bar{t}$ micrometres.

Use an algebraic method to calculate the range of values of $\bar{t}$ for which the null hypothesis would be rejected.[3]
State the conclusion of the test if $\bar{t}=56.9$. [2]

Accepted Answer

Reject $H_0$ if $\bar t\le 56.4$ or $\bar t\ge 57.2$ (3 s.f.); insufficient evidence at the 5% level for $\bar t=56.9$.

2013 JJC P2 Q6

2013 JJC P2 Q6

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