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Unformatted text preview: STA3032 (Section 7393) FINAL EXAM SOLUTION 1. What is the right interpretation of the given fitted vs residual plot?10 10 20 3050 50 Fitted vs Residual plot fit res • (a) It’s showing nonconstant variance. : It shows the increasing variance, thus squareroot transformation of Y might make the variance stable. 2. In simple linear regression, what is the distribution of the slope hatwide β 1 ? • (d) Normal distribution with the mean β 1 and the variance σ 2 P n i =1 ( x i ¯ x ) 2 1 3. To monitor the manufacturing process of rubber support bearing used between the superstructure and foundation pads of nuclear power plant, a quality control engineer samples 100 bearings from the production line each day over a 15day period. The summary data is ∑ n i =1 hatwide p i = ∑ n i =1 x i m = 0 . 48. What is the Lower Control Limit and the Upper Control Limit for such a mean proportion? • (a) (0, 0.0848) n = 15 ,m = 100 , ¯ p = ∑ n i =1 hatwide p i n = . 48 15 = 0 . 032 Lower Limit : ¯ p − 3 radicalbigg ¯ p (1 − ¯ p ) m = 0 . 032 − 3 radicalbigg . 032(1 − . 032) 100 = − . 0208 ⇒ Lower Limit = 0 Upper Limit : ¯ p + 3 radicalbigg ¯ p (1 − ¯ p ) m = 0 . 032 + 3 radicalbigg . 032(1 − . 032) 100 = 0 . 0848 4. The number of noticeable defects found by quality control inspectors in a randomly selected 1squaremeter specimen of woolen fabric from a certain loom is recorded each hour for a period of 20 hours. The summary data is ∑ n i =1 c i = 151. What is the Lower Control Limit and the Upper Control Limit for the number of defects? • (b) ( 0, 15.7932) n = 20 ¯ c = ∑ n i =1 c i n = 151 20 = 7 . 55 Lower Limit : ¯ c − 3 √ ¯ c = 7 . 55 − 3 √ 7 . 55 = − . 693179 ⇒ Lower Limit = 0 Upper Limit : ¯ c + 3 √ ¯ c = 7 . 55 + 3 √ 7 . 55 = 15 . 79318 5. Suppose that from the process for manufacturing electrical shafts, the lower and upper control limits for ¯ xchart is (116.149, 127.851). However, sample number 7 (the 7th samples) has ¯ x = 129, sample number 14 has ¯ x = 128, sample number 21 has ¯ x = 132, sample number 28 has ¯ x = 128 and sample number 35 has ¯ 127. Which of the statement is appropriate? • (b) There is a pattern in this process, thus the process is out of control. : Every 7th samples are outside of Control Limits. Thus there is a patteren, therefore the process is out of control....
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This note was uploaded on 07/18/2011 for the course STA 3032 taught by Professor Kyung during the Spring '08 term at University of Florida.
 Spring '08
 Kyung
 Statistics, Variance

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