Question

A certain reaction was run several times using each of two catalysts, A and B. The catalysts were supposed to control the yield of an undesirable side product. Results, in units of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows: Catalyst A 4.4,3.4,2.6,3.8,4.9,4.6,5.2,4.7,4.1,2.6,6.9,0.8,3.6,2.9,2.6,4.0,4.3 .9,4.8,4.5,4.4,3.1,5.7,4.5 Catalyst B .4,1.1,2.9,5.5,6.4,5.0,5.8,2.5,3.7,3.8,3.1,1.6, 3.5,5.9,6.7,5.2, 6.3, 2.6,4.3, 3.8 a. Construct a histogram for the yields of each catalyst. b. Construct comparative boxplots for the yields of the two catalysts. c. Using the boxplots, what differences can be seen between the results of the yields of the two catalysts A and B?

Answer 1

Answer:

a) See the code and the figure attached below

b) See the code and the figure attached below

c) We see significant differences on the boxplots. For Catalyst A the variation is less than the variation for Cat B. For both categories we see that we don't have a symmetric distributions. The maximum for Cat A is a little higher than the maximum for Cat B. The median for Cat A is a little higher than Cat B. And the third quartile for Cat A is lower than the third quartile for Cat B.

Step-by-step explanation:

Data given

Catalyst A: 4.4,3.4,2.6,3.8,4.9,4.6,5.2,4.7,4.1,2.6,6.9,0.8,3.6,2.9,2.6,4.0,4.3 .9,4.8,4.5,4.4,3.1,5.7,4.5

Catalyst B: .4,1.1,2.9,5.5,6.4,5.0,5.8,2.5,3.7,3.8,3.1,1.6, 3.5,5.9,6.7,5.2, 6.3, 2.6,4.3, 3.8

Solution to the problem

We are going to use R in order to do the plots required, we put the code and the output its attached to the solution.

Part a

R Code:

> catA<-c(4.4,3.4,2.6,3.8,4.9,4.6,5.2,4.7,4.1,2.6,6.9,0.8,3.6,2.9,2.6,4.0,4.3,0.9,4.8,4.5,4.4,3.1,5.7,4.5 )

> length(catA)

[1] 24

> catB<-c(.4,1.1,2.9,5.5,6.4,5.0,5.8,2.5,3.7,3.8,3.1,1.6,3.5,5.9,6.7,5.2,6.3,2.6,4.3,3.8 )

> length(catB)

[1] 20

> hist(catA)

> hist(catB)

Part b

R code:

> par(mfrow=c(1,2))

> boxplot(catA,main="Boxplot for CatA")

> boxplot(catB,main="Boxplot for CatB")

The result is attached.

Part c

We see significant differences on the boxplots. For Catalyst A the variation is less than the variation for Cat B. For both categories we see that we don't have a symmetric distributions. The maximum for Cat A is a little higher than the maximum for Cat B. The median for Cat A is a little higher than Cat B. And the third quartile for Cat A is lower than the third quartile for Cat B.