Loading the ToothGrowth data

library(datasets); data("ToothGrowth")

Performing basic exploratory data analyses

library(ggplot2)
g <- ggplot(ToothGrowth, aes(dose, len)) + geom_point() + geom_smooth(method = "lm") + facet_grid(.~supp)
g <- g + xlab("Dose in milligrams/day") + ylab("Tooth length") 
g <- g + ggtitle("Supplement type (OJ or VC)")
g

Providing a basic summary of the data

library(dplyr)

by_supp <- group_by(ToothGrowth, supp)
s <- summarize(by_supp, mean(len))
s

## Source: local data frame [2 x 2]
## 
##     supp mean(len)
##   (fctr)     (dbl)
## 1     OJ  20.66333
## 2     VC  16.96333

It can be seen that, the mean of tooth length for orange juice (OJ) is 20.6633333 and is greater than the mean of tooth length for Vitamin C (VC) which is 16.9633333.

Computing the confidence interval

Now we compute the 95% confidence interval on the difference of mean between tooth length for OJ and tooth length for VC.

t.test(len ~ supp, paired = TRUE, data = ToothGrowth)$conf

## [1] 1.408659 5.991341
## attr(,"conf.level")
## [1] 0.95

lower <- t.test(len ~ supp, paired = TRUE, data = ToothGrowth)$conf[1]
upper<- t.test(len ~ supp, paired = TRUE, data = ToothGrowth)$conf[2]
int <- paste("(",lower,", ",upper,")", sep = "")

Conclusion

The interval = (1.40865864101199, 5.99134135898801). Since the entire interval is above zero, therefore it is statistically significant to show that the mean of tooth length for OJ is greater than the mean of tooth length for VC at 95% confidence level.

Assumptions

By computing this confidence interval, we assume that tooth length for OJ and VC is normally distributed.