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Unformatted text preview: Practice Questions 6 QUESTIONS 1 THROUGH 3 ARE BASED ON THE FOLLOWING INFORMATION: Let 1 X , 2 X , 3 X , and 4 X be a random sample of observations from a population with mean μ and variance 2 σ . Consider the following two point estimators of μ : 1 ˆ θ = 0.10 1 X + 0.40 2 X + 0.40 3 X + 0.10 4 X and 2 ˆ θ = 0.20 1 X + 0.30 2 X + 0.30 3 X + 0.20 4 X 1. Which of the following is true? A) 1 ˆ θ is biased, but 2 ˆ θ is unbiased estimator of μ . B) 1 ˆ θ is unbiased, but 2 ˆ θ is biased estimator of μ . C) Both 1 ˆ θ and 2 ˆ θ are unbiased estimators of μ . D) Both 1 ˆ θ and 2 ˆ θ are biased estimators of μ . 2. Which of the following is true? A) Var ( 1 ˆ θ ) = Var( 2 ˆ θ ). B) Var ( 1 ˆ θ ) > Var( 2 ˆ θ ). C) Var ( 1 ˆ θ ) < Var( 2 ˆ θ ). D) Cannot tell the relationship between Var ( 1 ˆ θ ) and Var ( 2 ˆ θ ). 3. Which of the following is true? A) The relative efficiency of 2 ˆ θ to 1 ˆ θ is 0.67. B) The relative efficiency of 1 ˆ θ to 2 ˆ θ is 1.30 C) 1 ˆ θ is the more efficient estimator of μ than 2 ˆ θ . D) 2 ˆ θ is the more efficient estimator of μ than 1 ˆ θ . 4. In a recent survey of 600 adults, 16.4% indicated that they had fallen asleep in front of the television in the past month. Which of the following intervals represents a 96% confidence interval for the population proportion? A) 0.137 to 0.192 B) 0.140 to 0.189 C) 0.133 to 0.195 D) 0.143 to 0.186 5. The amount of material used in making a custom sail for a sailboat is normally distributed. For a random sample of 15 sails, you find that the mean amount material is 912 square feet, with a standard deviation of 64 square feet. Which of the following represents a 99% confidence interval for the population mean amount of material used in a custom sail?...
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This note was uploaded on 10/25/2010 for the course ECO 329 taught by Professor K during the Spring '08 term at University of Texas at Austin.
 Spring '08
 K

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