From Paper 3: Statistics and Mechanics
610 marks
The lengths of bolts made by a machine are normally distributed with standard deviation 3 mm. The mean length should be 25 mm. A random sample of 16 bolts has mean length 26.4 mm.
(a) Test, at the 1% level of significance, whether the mean length differs from 25 mm.
(b) Find the critical region for the sample mean in this test.
(c) Explain why it is important that the sample is random.