Chapter 06 - 103 Chapter 6 Chapter 6 Chapter 6 Chapter 6...

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Unformatted text preview: 103 Chapter 6 Chapter 6 Chapter 6 Chapter 6 Point Estimation Fill-in-the-Blank Questions Section 6.1 1. The objective of __________ is to select a single number such as 2 or s x , based on sample data, that represents a sensible value (good guess) for the true value of the population parameter, such as 2 or µ σ . ANSWER: point estimation 2. Given four observed values: 1 2 3 4 4.6, 6.2, 3.7, and 5.5, x x x x = = = = would result in a point estimate for µ that is equal to __________. ANSWER: 5 3. An estimator that has the properties of __________ and __________ will often be regarded as an accurate estimator. ANSWER: unbiasedness, minimum variance 4. A point estimator ˆ θ is said to be an __________ estimator of ˆ θ if ˆ ( ) E θ θ = for every possible value of θ . ANSWER: unbiased 5. The sample median µ %and any trimmed mean are unbiased estimators of the population mean µ if the random sample from a population that is __________ and __________. ANSWER: continuous, symmetric 6. Among all estimators of parameter θ that are unbiased, choose the one that has minimum variance. The resulting ˆ θ is called the __________ of θ . ANSWER: minimum variance unbiased estimator (MVUE) CHAPTER SIX 104 7. The standard error of an estimator ˆ θ is the __________ of ˆ θ . ANSWER: standard deviation Section 6.2 8. In your text, two important methods were discussed for obtaining point estimates: the method of __________ and the method of __________. ANSWER: moments, maximum likelihood 9. Let 1 , , n X X L L be a random sample from a probability mass function or probability density function f ( x ). For k = 1,2,3,……, the k th population moment is denoted by __________, while the k th sample moment is __________. ANSWER: 1 ( ),(1 / ) n k k i i E X n X = ∑ 10. Let 1 , , n X X L L be a random sample of size n from an exponential distribution with parameter λ . The moment estimator of ˆ is λ λ = __________. ANSWER: 1/ X 11. Let 1 2 ˆ ˆ ˆ , , , n θ θ θ L L be the maximum likelihood estimates (mle’s) of the parameters 1 2 , , , n θ θ θ L L . Then the mle of any function h ( 1 2 , , , n θ θ θ L L ) of these parameters is the function 1 2 ˆ ˆ ˆ ( , , , ) m h θ θ θ L L of the mle’s. This result is known as the __________ principle. ANSWER: invariance Point Estimation 105 Multiple-Choice Questions Section 6.1 12. Which of the following statements are true? A. A point estimate of a population parameter θ is a single number that can be regarded as a sensible value of θ . B. A point estimate of a population parameter θ is obtained by selecting a suitable statistic and computing its value from the given sample data. The selected statistic is called the point estimator of θ ....
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This note was uploaded on 07/20/2009 for the course MATH 3502 taught by Professor Zahra during the Summer '09 term at Carleton CA.

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Chapter 06 - 103 Chapter 6 Chapter 6 Chapter 6 Chapter 6...

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