Midterm II
1. A sailmaker testing 4 different spinnaker designs tested the designs together on 4 different days. On each day, the spinnakers were randomly assigned to boats of similar design. All boats were then tested on a 10-mile downwind course. The average speed was recorded and results appear below.
| Spinnaker Design Data | ||||
| Design | ||||
| Day | 1 | 2 | 3 | 4 |
| 1 | 9.7 | 10.8 | 10.7 | 12.0 |
| 2 | 4.5 | 5.1 | 5.3 | 6.0 |
| 3 | 13.0 | 14.5 | 15.2 | 18.0 |
, identify any pairwise differences among spinnaker designs using the most efficient method available.
2. Suppose a sample of buses will be chosen from a fleet and a set of oil analyses will be conducted on each bus. The variation in the response variable (Total Particle Concentration in parts per million) between buses is 200 ppm while variation within buses is 150 ppm. The cost of including a bus in the study is $300 while the cost of each additional analysis is $50. For a $5000 budget, how many buses should be included in the study and how many samples per bus will be taken?
3. Consider the experiment above. Suppose seven buses are sampled and 4 oil changes are completed on each one, yielding the following data:
| Bus Data | ||||||
| Bus ID | ||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 235 | 1030 | 350 | 65 | 70 | 120 | 650 |
| 160 | 450 | 420 | 130 | 70 | 160 | 360 |
| 90 | 750 | 190 | 100 | 95 | 135 | 280 |
| 280 | 900 | 260 | 40 | 160 | 215 | 900 |
4. The amount of toluene (in parts per million) from samples at 8 randomly selected wells is recorded below. The wells are classified by whether they are background wells, impacted wells or wells being tested for compliance. Analyze the data as a one factor fixed effects model, keeping in mind that the researchers are particularly interested in whether compliance wells are similar to background wells.
| Background | Impacted | Compliance |
| .5 | 200 | 1.2 |
| .5 | 2000 | 180 |
| .5 | ||
| .5 |