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CS 5014 Jain Test

Due November 12

The questions below are based on the data available
here. This data shows time in seconds
for execution of two programs (T1 and T2) on each of 24 test
problems. The data file also record problem size (small or large)
and problem type (smooth or nonsmooth) for each problem.

- Ignore problem size and type for the moment, i.e., treat each column
as one big sample of size 24 for each program. Test to see if
one program is significantly faster than the other when the data are viewed
in this way. Is there a
significant difference at a 90% confidence level? At a 95% confidence level?

- Now group the data into four classes according to the four possible
combinations of problem size and type. Is there a statistically significant
difference in the performance of the programs on any of the four classes,
when each is viewed as a separate sample?

- If we treat the data as coming from a `2
^{2} r' factorial design
with replications (as in Chapter 18 of Jain), we can compute
a model for the performance of each program as a function of
the two factors, problem size and type. Do this. Compute the
effects, the allocation of variation, and
90% confidence intervals for the effects.