The lengths, in centimetres, of worms of a certain kind are normally distributed with mean $$\(\mu\)$$ and standard deviation 2.3. An article in a magazine states that the value of $$\(\mu\)$$ is 12.7 . A scientist wishes to test whether this value is correct. He measures the lengths, $$\(x \mathrm{~cm}\)$$, of a random sample of 50 worms of this kind and finds that $$\(\sum x=597.1\)$$. He plans to carry out a test, at the $$\(1 \%\)$$ significance level, of whether the true value of $$\(\mu\)$$ is different from 12.7 . State, with a reason, whether he should use a one-tailed or a two-tailed test. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

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