QUESTION 1 PART 1 Given a simple random sample of size n from a Normal population with mean , and standard deviation , select the pair of hypotheses that can be tested in order to answer the following question: "is , different from 500?" (a) HO: #=500 , HI: # > 500 (b) HO: # =500 , H1: # 6 (b) HO: / =6 , H1: / 3 If G is known, and the observed value of the test statistic is 1.94, determine the p-value of the test (give answers correct to 3 decimal places). QUESTION 4 Given a simple random sample of size n = 22 from a Normal population with mean , and standard deviation , we test the hypotheses HO: / =300 HI: # # 300 If G is unknown, and the observed value of the test statistic is 2.01, determine the p-value of the test (give answers correct to 3 decimal places).QUESTION 5 Given a simple random sample of size n = 18 from a Normal population with mean , and standard deviation , we test the hypotheses HO: / = 250 HI: # # 250 at the 5% significance level. If 8 at the 5% significance level. If 6 is unknown, and the sample mean and sample variance are X=10.3, $2=13.4 determine the result of the test. O (a) The test rejects HO in favour of H1. O (b) The test does not reject HO in favour of H1. O (c) More information is required to determine the result of the test.QUESTION 8 In a case of `failure-terminated' lifetime testing, 15 failures are observed in a total operation time T = 178.2 hrs. Assume that the failure times are independent Exponential random variables with mean . You seek to conduct a chi-square test of the hypotheses HO: H = 9 H1: [ > 9. What is the observed value of the test statistic X ? (give answers correct to 3 decimal places) QUESTION 9 In a case of 'failure-terminated' lifetime testing, 15 failures are observed in a total operation time T = 178.2 hrs. Assume that the failure times are independent Exponential random variables with mean . You seek to conduct a chi-square test of the hypotheses HO: H = 9 H1: [ > 9. Evaluate the p-value of the test. (give answers correct to 3 decimal places) QUESTION 10 Given a simple random sample of size n = 200 from a non-Normal population with mean wand standard deviation o, we conduct a large sample z-test of the hypotheses HO: H = 2.4 H1: p # 2.4 If o is unknown, and the observed value of the test statistic is -1.86, determine the p-value of the test (give answers correct to 4 decimal places)