*Enter your name and EID here*

**This homework is due on Jan. 29, 2019 at 4:00 pm. Please submit as a pdf file on Canvas.**

This homework uses the `ToothGrowth`

dataset. This dataset is built into R, and it contains the lengths (`len`

) of odontoblasts (cells responsible for tooth growth) in 60 quinea pigs. Each animal received one of the three dose levels (`dose`

) of vitamin C in mg/day: 0.5, 1, or 2. Vitamin C was delivered either through orange juice or through ascorbic acid supplement (`supp`

).

`head(ToothGrowth)`

```
## len supp dose
## 1 4.2 VC 0.5
## 2 11.5 VC 0.5
## 3 7.3 VC 0.5
## 4 5.8 VC 0.5
## 5 6.4 VC 0.5
## 6 10.0 VC 0.5
```

**Problem 1: (4 pts)** We are interested in testing the effects of vitamin C on odontoblasts growths in guinea pigs. Since there are three different doses of vitamin C in the data set, and therefore three groups of length measurements, we will use an analysis of variance (ANOVA) test. Conduct an ANOVA test and interpret your results in 1-2 sentences. HINT: You will first need to create a linear model object using the `lm()`

function before you can use the `anova()`

function.

`# R code goes here`

Your answer goes here. 1-2 sentences only.

**Problem 2: (3 pts)** Create a boxplot of the teeth growth, separated by vitamin C doses. Based on this plot, do you expect the mean length of odontoblasts for the 2 mg/day dose to be the same or different than the mean length of odontoblasts for the 0.5 mg/day dose? Explain your answer.

`# R code goes here`

Your answer goes here. 1-2 sentences only.

**Problem 3: (3 pts)** Use a t test to determine if the mean length of odontoblasts for the 2 mg/day dose is the same as or different from the mean length of odontoblasts for 0.5 mg/day. Interperet and explain your results in 1-2 sentences.

`# R code goes here`

Your answer goes here. 1-2 sentences only.