Refer to Exercise 8.48. Suppose that Y1, Y2,..., Yn is a sample of size n from a
Chapter 8, Problem 8.49(choose chapter or problem)
Refer to Exercise 8.48. Suppose that Y1, Y2,..., Yn is a sample of size n from a gammadistributed population with parameters and . a If = m, where m is a known integer and is unknown, find a pivotal quantity that has a 2 distribution with m n df. Use this pivotal quantity to derive a 100(1)% confidence interval for . b If = c, where c is a known constant but not an integer and is unknown, find a pivotal quantity that has a gamma distribution with parameters = cn and = 1. Give a formula for a 100(1 )% confidence interval for . c Applet Exercise Refer to part (b). If = c = 2.57 and a sample of size n = 10 yields y = 11.36, give a 95% confidence interval for . [Use the appletGamma Probabilities and Quantiles to obtain appropriate quantiles for the pivotal quantity that you obtained in part (b).]
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