A machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discs gave a mean diameter, = 14.9 mm and a standard deviation, s = 1.33 mm. A test was carried out at the 5% level of significance to determine whether the machine is in good working order. Assume that the diameter of the disc follows a normal distribution.

1. State, in symbols, the null and alternate hypotheses for this test.
2. State, with reasons, whether a t-test or a z-test will be appropriate.
3. (Determine the rejection region(s) of the test. 4.
4. Calculate the value of the test statistic.
5. State, with reason, a valid conclusion for the test.