One biology study compares how quickly hairs on roots of a particular plant absorb water when they are placed in different environments. For each of eleven plants, the rates of influx of water for the root hair are measured under two distinct temperatures. The data is given below. For each pair, the "Temp 2" number is bigger than the "Temp 1" number, so even without a test it's clear that roots take in water more quickly under Temp 2. But how much more quickly? A test on the difference of the rates might be considered.

Plant Temp 1 Temp 2

A 0.89 2.13

B 0.49 1.16

C 0.91 2.60

D 0.80 1.58

E 0.56 1.53

F 0.79 1.70

G 0.47 2.67

H 0.50 2.64

I 1.08 2.19

J 1.65 2.54

K 1.94 4.46

Table 2: Plant root hair absorption data. Rates are in cubic microns per square micron per minute.

(a) Draw a graph and convince the researcher that a paired t-test may not be the best method for this data.(with R code)

(b) Explain why we should not take the logs of these differences (Temp1 minus Temp2.)