Duality of confidence interval and hypothesis testing means the equivalence of the two statements: (1) We fail to reject Ho : 0 interval for the parameter 0 contains the pre-hypothesized value 0. Answer the following questions by your understanding of the facts. 0o in a two-sided test; (2) The confidence (a) Explain why such a duality holds for one-sample z test and one-sample t test. (b) Explain why such a duality does not hold for one-proportion z test. (c) Does the duality apply to x test for population variance? Justify your answer.