Question 2 [21 marks] a) A machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discs gave a mean diameter, x = 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. i . State, in symbols, the null and alternate hypotheses for this test. [2] ii . State, with reasons, whether a f-test or a z-test will be appropriate. [3] iii. (Determine the rejection region(s) of the test. [3] iv . Calculate the value of the test statistic. [3] v. State, with reason, a valid conclusion for the test. [2] a) Persons who visit the restroom of a certain fast-food outlet were asked to state their opinion of the quality of the restroom facilities, The following tables show the responses from a sample of 100 persons. Gender of Respondent Totals Male Female Quality of Above Average 8 7 15 Facilities Average 26 24 50 Below Average 7 28 35 Totals 41 59 100 A x' test is carried out to determine whether there is an association between the gender of persons and their opinion. 1 ) State appropriate null and alternative hypotheses [2] ii ) Determine the critical region of the test at the 1% level of significance [1] iii) Calculate the expected value for Male and below average [2] iv) For a test statistic of 9.825, explain with reason, the conclusion of your test. [3]