Due Thursday, November 16 at the beginning of class

65 Points

**1.** [15 points] Navidi Chapter 9, Supplementary Exercise 2

**2.** [15 points] Navidi Chapter 9, Supplementary Exercise 6.

**3.** [15 points] Navidi Chapter 9, Supplementary Exercise 8.

**4.** [20 points]
Consider the following data.

Prob Size Type T1 T2 ------------------------------ 1 small smooth 5 7 2 large nonsmooth 19 13 3 small smooth 6 7 4 small nonsmooth 6 7 5 small nonsmooth 5 7 6 large smooth 12 14 7 small nonsmooth 7 6 8 small nonsmooth 7 8 9 small nonsmooth 5 7 10 large smooth 13 12 11 large smooth 14 10 12 small nonsmooth 6 7 13 large smooth 12 12 14 small smooth 6 6 15 large smooth 10 13 16 small smooth 7 5 17 large smooth 11 10 18 large nonsmooth 18 13 19 large nonsmooth 17 15 20 small smooth 6 6 21 large nonsmooth 18 14 22 small smooth 7 6 23 large nonsmooth 19 12 24 large nonsmooth 17 13

These data show 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, 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.