Question

Aw, rats! A nutrition experimenter intends to compare the weight gain of newly weaned male rats fed Diet $A$with that of rats fed Diet $B$. To do this, she will feed each diet to $10$rats. She has available $10$rats from one litter and $10$rats from a second litter. Rats in the first litter appear to be slightly healthier.

a. If the $10$rats from Litter $1$were fed Diet $A$, then genetics and type of diet would be confounded. Explain this statement carefully.

b. Describe how to randomly assign the rats to treatments using a randomized block design with litters as blocks.

c. Use technology or Table $D$to carry out the random assignment.

Short answer

(a) The differences between Litter $1$and the other litter are due to genetics or diet if all of the rats in Litter $1$were fed Diet $A$because the two litters differ both in diet and genetics.

(b) The $5$rats from litter $1$are randomly assigned to diet $A$, while $5$rats from litter $2$are randomly assigned to diet $A$. Diet $B$is given to the remaining rats.

(c) The Answer could vary according to litter $1$and$2$.

Step-by-step solution

Part (a) Step 1: Given information

We need to explain the statement "Genetics and diet type would be confounded if the$10$rats from litter$1$were fed diet$A$.

Part (a) Step 2: Explnation

We know that

• When the effects of two variables on the same response variable cannot be distinguished, they are said to be confused.
• We wouldn't know if the differences between Litter one and the other litter are due to genetics or diet if all of the rats in Litter one were fed Diet $A$, because the two litters differ both in diet and genetics.

As a result, we cannot distinguish between the impacts of genetics and the kind of diet on the response variable, implying that they are confused.

Part (b) Step 1: Given information

We need to find the reason for randomly assigning the rats to treatments using a randomized block design with litters as blocks.

Part (b) Step 2: Explanation

We know that

• A randomized block experiment divides the experimental units into two or more blocks based on a common trait and then assigns a treatment to each block at random.
• We'll utilize the litters as blocks because various litters have varied genotypes that could alter the outcomes.
• The five rats from litter one are randomly assigned to diet $A$, while five rats from litter two are randomly assigned to diet $A$. Diet B is given to the remaining rats.

Compare the rats' health in each block (litter) and for each diet variety.

Part (c) Step 1: Given information

We need to carry out the random assignment.

Part (c) Step 2: Explanation

We will assign a no. between one to ten in each of litter one and litter two.

Let the row chosen from table $D$is$124$.

$7103509001433674949772719967582761191596$

In litter one,

Let us choose the first digit, and five unique rats were chosen for diet $A$

Number	Selected rat	Assigned value
$7$	Selected	$\#7$
$1$	Selected	$\#1$
$0$	Selected	localid="1653768644072" $\#10$
$3$	Selected	$\#3$
$5$	Selected	$\#5$

Therefore, values assigned to rat in diet $A$are $\#1,\#3,\#5,\#7,\#10$and that assigned to diet $B$are $\#2,\#4,\#6,\#8,\#9$.

In litter two,

Similar to litter one value are assigned to the rats.

Therefore, values assigned to rat in diet $A$are $\#1,\#3,\#4,\#9,\#10$and that assigned to diet $B$are$\#2,\#5,\#6,\#7,\#8$.