252HW1Soln - Statistics 252 Homework#1 Solutions Summer...

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Statistics 252 – Homework #1 Solutions – Summer 2011 STAT 252 Homework 1 Solutions (65 marks) – Due Monday, July 11 by 10pm 1. (4 marks) Suppose n s c m = . a) (2 marks) Solve for c (as a function of m, n and s ). mn c s mn c s ⇒= b) (2 marks) Solve for n (as a function of c, m and s ). 2 s cs n m cs n m ⎛⎞ ⎜⎟ ⎝⎠ 2. (3 marks) Suppose ) 2 /( = n s s t f and t s t p = . Express f as a function of p and n . () / (2 ) ) /( 2) / ( 2) 1 ts tst fn n sn s s t p n p −− ⎧⎫ == −= ⎨⎬ ⎩⎭ =− 3. (2 marks) If f ( x ) = a + bx , what is f ( x + k ) – f ( x ) ? ( ) { } { } f x ka b x b x b k f x k f x a bx bk a bx bk += + ++ ⇒+ = + + + = 4. (2 marks) If f ( x 1 , x 2 ) = a + bx 1 + cx 2 + dx 1 x 2 , what is f ( x 1 + k , x 2 ) – f ( x 1 , x 2 ) ? 12 1 212 1 2 2 1 2 1 2 2 1 2 1 2 2 (, ) ) ( , ) ={ } { } fx kx a bx k c x dx kx ab x b kc x d x k x fxx a bx bk cx dx x dkx a bx cx dx x bk dkx + + + + + + = + +++ = =+
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Statistics 252 – Homework #1 Solutions – Summer 2011 5. (5 marks) An experiment was conducted to compare the effects of two teaching styles for grade 12 mathematics. The individuals in the experiment were grade 12 math students from one particular high school. The students were randomly assigned to the two treatment groups. After a three-week course, all students took an identical standardized exam. The response was the students score on the exam. a) (1 mark) What is the population of interest? All grade 12 math students. b) (2 marks) Can we make population inferences? If so, did you need to make any assumptions? No, since we do not have random selection from the population of interest. OR Yes, if we assume that the grade 12 math students from this school are representative of all grade 12 math students, then population inferences may be ok. c) (2 marks) Can we make causal inferences? That is, can we conclude that any difference in exam scores was caused by the difference in teaching styles? Yes, since we have random allocation to the treatment groups, we can conclude that the differences in exam scores were caused by the difference in teaching styles.
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This note was uploaded on 07/31/2011 for the course STAT 252 taught by Professor Paulcartledge during the Summer '11 term at University of Alberta.

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252HW1Soln - Statistics 252 Homework#1 Solutions Summer...

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