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Unformatted text preview: Statistics 103: Lab 9 LAB PROBLEMS 1. Let X and Y be two random variables such that Y = + X + Z where Z is independent of X and Z N (0 , 2 ). A random sample of size n = 15 from ( X,Y ) resulted in the following statistics: X = 10 . 0897 (1) Y = 70 . 2221 (2) 15 X i =1 ( X i X ) 2 = 16 . 7527 (3) 15 X i =1 ( X i X ) Y i = 30 . 5332 (4) Find , . If 2 = 3 . 7272 what is your estimated standard deviation of and ? answer: = 1 . 8226 , = 51 . 8327 ; . 4717 , 4 . 7852 2. Referring to the data in the problem 1 which of the following intervals best summarizes the likely values of the true : (1 . 8 , 2 . 3) 1 . 8226 4 1 . 8226 . 4717 1 . 8226 1 . 9306 answer: 1 . 8226 . 4717 3. Referring to the data in the problem 1 which of the following intervals best summarizes the likely values of the true : (50 , 60) (46 , 56) (25 , 75) 51 . 8327 1 . 9306 answer: (46 , 56) 4. Which of the following conclusions follow from the data presented in problem 1: There is strong evidence that > There is weak evidence that > The data is consistent with = 0 answer: There is strong evidence that > 5. Which of the following conclusions follow from the data presented in problem 1: There is strong evidence that < 2 There is weak evidence that < 2 The data is consistent with = 2 answer: The data is consistent with = 2 6. Which of the following conclusions follow from the data presented in problem 1: There is strong evidence that < 61 There is weak evidence that < 61 The data is consistent with = 61 answer: There is weak evidence that < 61 7. Consider randomly picking a married couple from Minnesota. Let W denoted the height of the wife (in inches) and let H denoted the height of the husband (in inches). Suppose H and W follow the regression model: H = 51 + 0 . 27 W + Z where Z is independent of W and Z N (0 , 6 . 83). (a) If W = 66 what do you predict the husbands height to be? (b) Of the husbands who are married to women 5 feet tall, what percentage are over 5 feet 8 inches tall? answer: 68.82; 37.83% Treatment A Treatment B Small Kidney Stones 81 / 87 = 93% 234 / 270 = 87% Large Kidney Stones 192 / 263 = 73% 55 / 80 = 69% Both 273 / 350 = 78% 289 / 350 = 83% TABLE I. Success rates for two treatments of two types of kidney stones. 8. This problem illustrates Sympsons Paradox which can occur when studying the relationship be tween two variables: Two medical procedures are being considered for the treatment of kidney stones. Kidney stones can be classified as either small or large. Table I displays some experimental results of the two treatments on small and large kidney stones. Based on the overall results (bottom row) it would seem that Treatment B is better. How ever, on closer inspection, Treatment A does better for both small kidney stones and for large kidney stones. How could this be?? 2 answer: Treatment A is more effective than Treat ment B in all cases so is clearly better. The reament B in all cases so is clearly better....
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This note was uploaded on 09/13/2011 for the course STA 103 taught by Professor Drake during the Spring '09 term at UC Davis.
 Spring '09
 Drake
 Statistics

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