## Homework 1

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.