```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## About this assignment  

- **Goal:** to review the concepts learned about treatment structure and design structure of split-plot experiments. 
- **Due:** Friday, July 18th. 

## 1

The data in `df` below correspond to an experiment grown in 1995-1996 at the Scottish Crop Research Institute. The treatment design was a 2x70 factorial, and the design structure was a split-plot design with 4 blocks, 2 whole-plot fungicide treatments, and 70 barley varieties. The total area was 10 rows (North/South) by 56 beds (East/West). 

```{r}
library(agridat)
data("durban.splitplot")
df <- durban.splitplot
```

### 1.a. 

Using math notation, write the statistical model to analyze that dataframe. Define all model components. 

### 1.b. 

Write an ANOVA table including source of variation and degrees of freedom. Include both the treatment and the design sources of variability. 

### 1.c. 

Fit the model in (1.a.) to the data using R software. 

### 1.d. 

Please provide the estimated treatment means for fungicide treatment "F1" and genotype "G42" and their 95% confidence intervals.  

### 1.e. 

Please provide the estimated variance components (i.e., the $\sigma$s in (1.a.). 





