assg 4 sol

assg 4 sol - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1306 INTRODUCTORY STATISTICS (SEMESTER 1 2008/2009) Suggestion Solution of Assignment 4 Question 1 Let X and Y be the costs of repairs by bumper guards 1 and 2 respectively. Then, we test the hypothesis H : & X & & Y = 0 vs H 1 : & X 6 = & Y : From the observations, we have x = 144 ; y = 149 ; s 2 X = 363 : 2 and s 2 Y = 202 : Assume that they have the same variance. The variance of pooled sample is s 2 P = (6 & 1) (363 : 2) + (6 & 1) (202) 6 + 6 & 2 = 282 : 6 : The compued test statistic is t = 144 & 149 p 282 : 6 r 1 6 + 1 6 = & : 5152 and the critical value is t 6+6 & 2 ; : 005 = 3 : 169 . Since the computed test statistic does not fall within the critical region, H cannot be rejected at 1% level of signi&cance. Therefore, we can conclude that no evidence is found indicating the di/erence in the costs of repairs by bumper guards 1 and 2. Question 2 Let D i be the di/erence between X i and Y i for i = 1 ; 2 ;:::; 16 , i.e. D i = X i & Y i . Now, we test the hypothesis H : & D = 0 vs H 1 : & D > : The computed di/erences are d i d i 13 6 7 1 & 1 4 5 3 3 2 2 6 & 1 12 4 1 The summary statistics are d = 4 : 125 ;s 2 D = 16 : 5167 ; and s D = 4 : 0641 : The computed test statistic is t = 4 : 125 4 : 0641 = p 16 = 4 : 0599 : At & = 5% , we see that t n & 1 ;& = 1 : 753 . It follows that H can be rejected using a one-sided signi&cance test with & = 0 : 05 and we may conclude that the exercises for...
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This note was uploaded on 09/06/2010 for the course STAT STAT1306 taught by Professor Prof during the Fall '08 term at HKU.

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assg 4 sol - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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