# Lab9 - Statistics 103: Lab 9 6. Which of the following...

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Statistics 103: Lab 9 LAB PROBLEMS 1. Let X and Y be two random variables such that Y = α + βX + 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 ˆ β , ˆ α . If ˆ σ 2 = 3 . 7272 what is your estimated standard deviation of ˆ β and ˆ α ? 2. Referring to the data in the problem 1 which of the following intervals best summarizes the likely values of the true β : (1 . 8 , 2 . 3) 1 . 8226 ± 4 1 . 8226 ± 0 . 4717 1 . 8226 ± 1 . 9306 3. Referring to the data in the problem 1 which of the following intervals best summarizes the likely values of the true α : (50 , 60) (46 , 56) (25 , 75) 51 . 8327 ± 1 . 9306 4. Which of the following conclusions follow from the data presented in problem 1: There is strong evidence that β > 0 There is weak evidence that β > 0 The data is consistent with β = 0 5. Which of the following conclusions follow from the data presented in problem 1: There is strong evidence that β < 2 There is weak evidence that β < 2 The data is consistent with β = 2 6. Which of the following conclusions follow from the data presented in problem 1: There is strong evidence that α < 61 There is weak evidence that α < 61 The data is consistent with α = 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? 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 “Sympson’s 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?? PRACTICE PROBLEMS 1. Let X and Y be two random variables such that Y = α + βX + Z where Z is independent of X and Z ∼ N (0 2 ). A random sample of size n = 25 from ( X,Y ) resulted

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2 in the following statistics: X = 0 . 0335 (5) Y = - 0 . 7713 (6) 25 X i =1 ( X i - X ) 2 = 27 . 2902 (7) 25 X i =1 ( X i - X ) Y i = - 269 . 1961
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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.

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Lab9 - Statistics 103: Lab 9 6. Which of the following...

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