**Analysis of the Oil Data Set**

A project from Fall 1999 involved heating motor oil until it caught on fire. There were eight runs in random order. Here is the description of the data:

- "conv" stands for conventional oil
- "syn" stands for synthetic oil
- "5/30" and "20/50" are two viscosities
- "time" is the time until catching fire

**Data:**

| Obs | Type | Vis | Time |
|-----|------|-----|------|
| 1 | conv | 5/30 | 345 |
| 2 | syn | 5/30 | 658 |
| 3 | conv | 20/50| 360 |
| 4 | syn | 20/50| 546 |
| 5 | conv | 5/30 | 360 |
| 6 | syn | 5/30 | 676 |
| 7 | conv | 20/50| 342 |
| 8 | syn | 20/50| 512 |

**Task:**

Run the linear model (lm) in Splus or M-Lab to get the ANOVA output using the full model:

\[ \text{model time} = \text{vis} + \text{type} + \text{vis} \times \text{type} \]

1. Determine if there is a mean difference in oil types (conv vs. syn):
- **p-value =**

2. Determine if there is a mean difference in viscosity levels (5/30 vs. 20/50):
- **p-value =**

3. Determine if there is an interaction between the factors:
- **p-value =**