Fibre Content in Breakfast Cereal
========================================================

Our hypothesis is that cereals sold on the top shelf, such as bran flakes and granola, appeal to adults and will have a *significantly* higher fibre content.  This is because cereals on the middle shelf tend to be sugary cereals, such as Froot Loops and Lucky Charms, that appeal to children, and the bottom shelf is dominated by less expensive cereals  such as Corn Flakes and Puffed Wheat.

```{r, message=FALSE}
require(MASS)
require(mosaic)
bwplot(fibre~factor(shelf), data=UScereal, xlab="Shelf",ylab="Fibre (g)",main="Fiber in Breakfast Cereal", col="dodgerblue")
```

Looking at the boxplot, it certainly does seem like Shelf #3, the top shelf, has a higher fibre content.  Let's compute some basic statistics.


```{r}
favstats(fibre~shelf,data=UScereal) #mosaic command
```

Now let's use ANOVA to see if this difference is statistically significant at the $\alpha=0.05$ level. Our null hypothesis states no difference between any of the shelves: $$H_0: \mu_1 = \mu_2 = \mu_3$$

```{r}
fibre.model<-lm(fibre~shelf,data=UScereal)
anova(fibre.model)
```

We see that the difference is statistically significant, as $F_{1,63}=9.25$ with $p=0.0034$.

Our conclusions (partially from the statistical analyses) are:
- The cereal sold on the top shelf has the highest fibre content.  We suspect that expensive cereals geared towards adults are usually found in this location.
- The cereal sold on the middle shelf tends to be highly sweetened and artificially colored cereals geared towards children and placed at their eye level.  Little kids don't want shredded wheat or bran flakes or dried fruit.
- The cereal sold on the bottom shelf is cheaper cereals and not as loaded with fibre as that on the top shelf.  Kroger doesn't really want us buying generic corn flakes or bagged puffed wheat.