A machine makes screws with a mean length of $$\(30 \mathrm{~mm}\)$$ and a standard deviation of $$\(2.5 \mathrm{~mm}\)$$. A manager claims that, following some repairs, the machine is now making screws with a mean length of less than $$\(30 \mathrm{~mm}\)$$. The manager takes a random sample of 80 screws and finds that they have a mean length of $$\(29.5 \mathrm{~mm}\)$$. Use a suitable test, at the 5\% level of significance, to determine whether there is evidence to support the manager's claim. State your hypotheses clearly. (5)

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