MS-Sol-EE-C17

MS-Sol-EE-C17 - CHAPTER 17 POPULATION PARAMETERS AND SAMPLE...

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CHAPTER 17 POPULATION PARAMETERS AND SAMPLE STATISTICS EXERCISE 17.1 Section 17.1 Random samples and sampling distributions (page 467) 1. (a) The possible samples of size 2 and their means are shown below. Sample Mean, x Sample Mean, x (0, 0) 0 (3, 6) 4.5 (0, 3) 1.5 (6, 0) 3 (0, 6) 3 (6, 3) 4.5 (3, 0) 1.5 (6, 6) 6 (3, 3) 3 (b) There are altogether 9 possible samples; each is equally likely to be drawn. Probability of drawing a specific sample = 9 1 (c) From the results in (a) and (b) , we obtain the following values of x together with their respective probabilities. x 0 1.5 3.0 4.5 6.0 ) ( P x X = 9 1 9 2 9 3 9 2 9 1 (d) The probability histogram is shown below. 33
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C HAPTER 17 P OPULATION P ARAMETERS AND S AMPLE S TATISTICS 2. (a) Sample Mean Sample Mean (2, 2) 2 (6, 2) 4 (2, 4) 3 (6, 4) 5 (2, 6) 4 (6, 6) 6 (2, 8) 5 (6, 8) 7 (4, 2) 3 (8, 2) 5 (4, 4) 4 (8, 4) 6 (4, 6) 5 (8, 6) 7 (4, 8) 6 (8, 8) 8 (b) The distribution of the sample mean X is shown in the following table: x 2 3 4 5 6 7 8 f x ( ) 1 16 2 16 3 16 4 16 3 16 2 16 1 16 (c) 3. (a) Sample Mean Sample Mean (1, 1) 1 (4, 8) 6 (1, 3) 2 (4, 9) 6.5 (1, 4) 2.5 (8, 1) 4.5 (1, 8) 4.5 (8, 3) 5.5 (1, 9) 5 (8, 4) 6 (3, 1) 2 (8, 8) 8 (3, 3) 3 (8, 9) 8.5 (3, 4) 3.5 (9, 1) 5 (3, 8) 5.5 (9, 3) 6 (3, 9) 6 (9, 4) 6.5 (4, 1) 2.5 (9, 8) 8.5 (4, 3) 3.5 (9, 9) 9 (4, 4) 4 34
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S ECTION 17.1 R ANDOM S AMPLES AND S AMPLING D ISTRIBUTIONS 35
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C HAPTER 17 P OPULATION P ARAMETERS AND S AMPLE S TATISTICS (b) The distribution of the sample mean X is shown in the following table. x 1 2 2.5 3 3.5 4 4.5 f x ( ) 1 25 2 25 2 25 1 25 2 25 1 25 2 25 x 5 5.5 6 6.5 8 8.5 9 f x ( ) 2 25 2 25 4 25 2 25 1 25 2 25 1 25 (c) P( X 5) = 2 25 + 4 25 + 2 25 + 1 25 + 2 25 + 1 25 = 12 25 4. (a) First throw Second throw 1 2 3 4 5 6 1 (1, 1) 1 (1, 2) 1.5 (1, 3) 2 (1, 4) 2.5 (1, 5) 3 (1, 6) 3.5 2 (2, 1) 1.5 (2, 2) 2 (2, 3) 2.5 (2, 4) 3 (2, 5) 3.5 (2, 6) 4 3 (3, 1) 2 (3, 2) 2.5 (3, 3) 3 (3, 4) 3.5 (3, 5) 4 (3, 6) 4.5 4 (4, 1) 2.5 (4, 2) 3 (4, 3) 3.5 (4, 4) 4 (4, 5) 4.5 (4, 6) 5 5 (5, 1) 3 (5, 2) 3.5 (5, 3) 4 (5, 4) 4.5 (5, 5) 5 (5, 6) 5.5 6 (6, 1) 3.5 (6, 2) 4 (6, 3) 4.5 (6, 4) 5 (6, 5) 5.5 (6, 6) 6 (b) The distribution of the sample mean X is: x 1 1.5 2 2.5 3 3.5 f x ( ) 36 1 2 36 3 36 4 36 5 36 6 36 x 4 4.5 5 5.5 6 f x ( ) 5 36 4 36 3 36 2 36 1 36 (c) (i) P 36 1 ) 6 ( = = X 36
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S ECTION 17.1 R ANDOM S AMPLES AND S AMPLING D ISTRIBUTIONS (ii) P(2 < X < 4) = P( X = 2.5 or 3 or 3.5) = 4 36 + 5 36 + 6 36 = 5 12 37
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C HAPTER 17 P OPULATION P ARAMETERS AND S AMPLE S TATISTICS 5. (a) (i) Samples of 2 observations and their probabilities are shown below. Sample Probability (0, 0) (0.3) 2 = 0.09 (0, 1) (0.3)(0.7) = 0.21 (1, 0) (0.7)(0.3) = 0.21 (1, 1) (0.7) 2 = 0.49 (ii) Sample mean, 2 x Probability 0 0.09 0.5 2 × 0.21 = 0.42 1.0 0.49 (b) (i) Samples of 3 observations and their probabilities are shown below. Sample
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This note was uploaded on 10/17/2011 for the course IELM 3010 taught by Professor Fugee during the Winter '11 term at HKUST.

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MS-Sol-EE-C17 - CHAPTER 17 POPULATION PARAMETERS AND SAMPLE...

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