Statistics 506
Test 1

1. A computer science major tests two sort routines (Quick sort and Bubble sort) on two different platforms (Pentium PC and Unix Sparcstation) for two different data set sizes (1000 elements and 10000 elements) using a factorial design. The data appear below:

   Factor settings Response (CPU seconds)

   (Bubble,PC,1000) 3.7

   (Quick,PC,1000) 1.2

   (Bubble,Unix,1000) 2.9

   (Quick,Unix,1000) 11.3

   (Bubble,PC,10000) 4.0

   (Quick,PC,10000) 9.1

   (Bubble,Unix,10000) 3.4

   (Quick,Unix,10000) 9.4

   1. Another student argued that this wasn't a statistical experiment since computer operations aren't random. Argue for or against this position.
   2. Compute the effects and draw a normal probability plot. What are your conclusions?
   3. The student had mis-keyed run 4-the response should have been 1.3 rather than 11.3. Revise your analysis in (b) to reflect this information. What are your conclusions?
2. The strength of a weld was measured in a 3-factor experiment as a function of Heating Time, Heating Temperature and Flux Material. The data appear below:

   Factor settings Response (Breaking strength)

   (L,L,A) 174

   (H,L,A) 77

   (L,H,A) 54

   (H,H,A) 172

   (L,L,B) 158

   (H,L,B) 34

   (L,H,B) 56

   (H,H,B) 137

   1. The attached probability plot indicates the presence of a strong interaction. Construct an interaction plot for AB (Time x Temperature) and interpret the plot.

      In light of the plot, the researcher thought that the experimental factors should have been Time, Energy and Flux material. Under this scheme, levels (L,L) and (H,H) for Time and Temperature would be Level 1 for Energy (inappropriate energy level) and levels (L,H) and (H,L) for Time and Temperature would be Level 2 for Energy (appropriate energy level). The data would be recoded as:

      Factor settings Response (Breaking strength)

      (L,1,A) 174

      (H,2,A) 77

      (L,2,A) 54

      (H,1,A) 172

      (L,1,B) 158

      (H,2,B) 34

      (L,2,B) 56

      (H,1,B) 137

   2. Recompute the effects and construct a normal probability plot. Compare the two analyses; which approach do you prefer?

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