题目
Problem
A machine makes screws with a mean length of 30 mm and a standard deviation of 2.5 mm.
A manager claims that, following some repairs, the machine is now making screws with a mean length of less than 30 mm. The manager takes a random sample of 80 screws and finds that they have a mean length of 29.5 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)
题目中文翻译
一台机器制造螺钉，其平均长度为 30 mm，标准差为 2.5 mm。
一位经理声称，在经过一些维修后，这台机器现在制造的螺钉平均长度小于 30 mm。经理随机抽取了 80 个螺钉，发现它们的平均长度为 29.5 mm。
使用合适的检验，在 5% 显著性水平下判断是否有证据支持经理的说法。清楚写出假设。