Overview

This project investigates the tooth growth data for Guinea pigs. using a 95% confidence interval it is shown that Orange Juice gives a mean growth gain of -0.17 to 7.6.

Data Summary

A summary for the data for teeth for OJ is:

oj = ToothGrowth[ToothGrowth$supp=='OJ',]
summary(oj)
##       len        supp         dose      
##  Min.   : 8.20   OJ:30   Min.   :0.500  
##  1st Qu.:15.53   VC: 0   1st Qu.:0.500  
##  Median :22.70           Median :1.000  
##  Mean   :20.66           Mean   :1.167  
##  3rd Qu.:25.73           3rd Qu.:2.000  
##  Max.   :30.90           Max.   :2.000
varOj = var(oj$len)

A summary for the data for teeth for VC is:

vc = ToothGrowth[ToothGrowth$supp=='VC',]
summary(vc)
##       len        supp         dose      
##  Min.   : 4.20   OJ: 0   Min.   :0.500  
##  1st Qu.:11.20   VC:30   1st Qu.:0.500  
##  Median :16.50           Median :1.000  
##  Mean   :16.96           Mean   :1.167  
##  3rd Qu.:23.10           3rd Qu.:2.000  
##  Max.   :33.90           Max.   :2.000
varVc = var(vc$len)

The variances are oj: 43.6334368 and vc: 68.3272299.

Analysis

A 95% T confidence interval is applied:

t.test(oj$len,vc$len,var.equal=F, paired=F)
## 
##  Welch Two Sample t-test
## 
## data:  oj$len and vc$len
## t = 1.9153, df = 55.309, p-value = 0.06063
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.1710156  7.5710156
## sample estimates:
## mean of x mean of y 
##  20.66333  16.96333

From this we can say with 95% confidence the average gain in tooth growth is between -0.17 and 7.6 when using Orange Juice vs Ascorbic Acid. This indicates that Orange Juice is likely a more effective delivery mechanism but does not rule out the difference being negligible.

Assumptions

I have assumed the variance between both sets is not equal since the sample variances were ~50% different.