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# ps2 - STAT 203 PROBLEM SET 2 Due date February 4 2010(1 In...

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STAT 203 PROBLEM SET 2 Due date: February 4, 2010 (1) In one-way ANOVA, the model is: Y ij = ± + ² i + ³ ij ; ³ i;j ± N (0 2 ) : The mean sum-of-treatment-squares term is MSTR = r X i =1 n i ± Y i ± ² Y ±± ² 2 = ( r ² 1) : Assume that n i = n , i.e. each level has n observations. Show the following: (a) For each i , Y i ± ² Y ±± = ² i + (± ³ i ± ² ± ³ ±± ) ; where ± ³ i ± = 1 n P n j =1 ³ ij and ± ³ ±± = 1 nr P r i =1 P n j =1 ³ ij (b) P r i =1 ± Y i ± ² Y ±± ² 2 = P ² 2 i + P ³ i ± ² ± ³ ±± ) 2 + 2 P ² i ³ i ± ² ± ³ ±± ), (c) E [2 P ² i ³ i ± ² ± ³ ±± )] = 0, (d) Use (a-c), and the fact E h X ³ i ± ² ± ³ ±± ) 2 i = ( r ² 1) ´ 2 n ; to show that E ( MSTR ) = ´ 2 + n P r i =1 ² 2 i r ² 1 : (2) In the surgery rehab data of lecture 8 (data ²le Rehab.txt), design and test the hypothesis that the recovery times of patients in the be- low and above average ²tness group have the same absolute deviation from the average group. Write out explicitly the null hypothesis and the way you conducted the test.

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ps2 - STAT 203 PROBLEM SET 2 Due date February 4 2010(1 In...

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