# CS5014 Fall 2006 Assignment 13 Due Thursday, November 16 at the beginning of class 65 Points

This assignment should be handed in typed using a word processor such as LaTeX or Microsoft Word. No handwritten work will be accepted.

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.

1. 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?
2. 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?
3. If we treat the data as coming from a `22 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.