# PracticeQuestions6Answers - 2 2 2 1 2 4 4 2 Var X Var X Var...

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Practice Questions 6 1. C 2. B 3. D 4. C 5. A 6. B 7. D 8. B 9. B 10. A 11. A 12. B 13. C 14. C 15. A 16. A 17. D 18. B 19. B 20. C 21. D 22. 1 / 2 , / n X t s n α - ± = 63.57 ± 2.032(17.32) / 5.92 = 63.57 ± 35 = 63.57 ± 5.95. Then, UCL = 69.52 and LCL = 57.62. 23. If independent random samples of size 35 are repeatedly selected from the population and 95% confidence intervals for each of these samples are determined, then over a very large number of repeated trials, 95% of these intervals will contain the value of the true average amount of money a typical college student spends per day during spring break. 24. 1 2 ( ) [ ( ) ( )]/ 2 ( ) / 2 E X E X E X μ = + = + = 1 2 ( ) [ ( ) 3 ( )]/ 4 ( 3 ) / 4 E Y E X E X = + = + = 1 2 ( ) [ ( ) 2 ( )]/ 3 ( 2 ) / 3 E Z E X E X = + = + = Since ( ) ( ) ( ) E X E Y E Z = = = , then all three estimators are unbiased. 25.
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Unformatted text preview: 2 2 2 1 2 ( ) [ ( ) ( )]/ 4 ( ) / 4 / 2 Var X Var X Var X σ = + = + = 2 2 2 1 2 ( ) [ ( ) 9 ( )]/16 ( 9 ) /16 5 /8 Var Y Var X Var X = + = + = 2 2 2 1 2 ( ) [ ( ) 4 ( ) / 9 ( 4 ) / 9 5 / 9 Var Z Var X Var X = + = + = Hence, X is the most efficient estimator since ( ) ( ) ( ) Var X Var Z Var Y < < . Note that 1 2 ( )/ 2 X X X X = + = , then, 2 2 ( ) ( ) / / 2 Var X Var X n = = = . 26. Relative efficiency of X with respect to Y = ( ) / ( ) Var Y Var X = (5 2 / 8) / ( 2 / 2) = 5 / 4 = 1.25 Relative efficiency of X with respect to Z = ( ) / ( ) Var Z Var X = (5 2 / 9) / ( 2 / 2) =10 / 9 = 1.11...
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