Hi, I need help with this statistics question. Please show the steps clearly. Thank you!

Problem 5. [13 pts] Duality of condence interval and hypothesis testing means the equivalence of the two statements: (1) We fail to reject H0 : I9 = 90 in a twosided test; (2) The condence interval for the parameter 6 contains the prehypothesized value 90. Answer the following questions by your understanding of the facts. (a) [4 pts] Explain why such a duality holds for onesample 2: test and onesample t test. (b) [4 pts] Explain why such a duality does not hold for oneproportion 2 test. (c) [5 pts] Does the duality apply to X2 test for population variance? Justify your