Question

Few people want to eat discolored french fries. To prevent spoiling and to preserve flavor, potatoes are kept refrigerated before being cut for french fries. But immediate processing of cold potatoes causes discoloring due to complex chemical reactions. The potatoes must therefore be brought to room temperature before processing. Researchers want to design an experiment in which tasters will rate the color and flavor of french fries prepared from several groups of potatoes. The potatoes will be freshly picked or stored for a month at room temperature or stored for a month refrigerated. They will then be sliced and cooked either immediately or after an hour at room temperature.

a. Identify the experimental units, the factors, the number of levels for each factor, and the treatments.

b. Describe a completely randomized design for this experiment using $300$potatoes.

c. A single supplier has made 300 potatoes available to the researchers. Describe a statistical benefit and a statistical drawback of using potatoes from only one supplier.

d. The researchers decided to do a follow-up experiment using potatoes from several different suppliers. Describe how they should change the design of the experiment to account for the addition of other suppliers.

Short answer

a. The experimental units, the factors, the number of levels for each factor, and the treatments is Freshly picked-Immediately
Stored at room temperature-Immediately
Stored refrigerated-Immediately
Freshly picked-after an hour
Stored at room temperature-after an hour
Stored refrigerated after an hour.

b. Let us assign a unique number between $1\mathrm{and}300$to each of the $300$potatoes.

c. A statistical benefit is less variability and a statistical drawback is the result is can't be generalized to all suppliers.

d. They should change the design of the experiment to account for the addition of other suppliers is use a randomized block design with regular potatoes in one block and sweet potatoes in another block. Assign the six treatments for each block in the same way done in part b.

Step-by-step solution

Part (a) step 1: Given Information

We need to identify the experimental units, the factors, the number of levels for each factor, and the treatments.

Part (a) step 2: Explanation

The experimental units are individuals on whom an experiment is performed.
Experimental. units$=$Potatoes were used in the experiment
The factors are variables whose levels are manipulated by an experimenter and these variables are controlled by the experimenter.

Factors $=$Storage method, Time till cooking (immediately, after an hour).
The levels are the possible values for a variable that is controlled by the experimenter.
Storage method has$3$ levels: freshly picked, stored at room temperature, stored refrigerated
Time till cooking has$2$ levels: immediately, after an hour
The treatments are what the subjects are subjected to. More precisely, the treatments are any combination of levels for the different factors.
Freshly picked-Immediately
Stored at room temperature-Immediately
Stored refrigerated-Immediately
Freshly picked-after an hour
Stored at room temperature-after an hour
Stored refrigerated-after an hour

Part (b) step 1: Given Information

We need to describe a completely randomized design for this experiment using $300$potatoes.

Part (b) step 2: Explanation

Consider:

$300$potatoes

Treatments: Freshly picked-Immediately, Stored refrigerated-Immediately, Stored at room temperature-Immediately, Freshly picked-after an hour, Store at room temperature-after an hour, Stored refrigerated-after an hour
The complete randomized experiment randomly assigns all subjects to a group.
Let us assign a unique number between $1\mathrm{and}300$(including) to each of the$300$ potatoes.
Randomly draw $60$unique numbers between $1\mathrm{and}300$(including), which could be done by using slips of papers, a random digits table or technology.

The 60 corresponding potatoes (to the$60$ selected integers) will be assigned to the Freshly picked-Immediately treatment.
Similarly, we assign $60$of the remaining potatoes to the Stored at room temperature-Immediately treatment, we assign $60$of the remaining potatoes to the Stored refrigerated-Immediately, we assign $60$of the remaining potatoes to the Freshly picked after an hour of treatment, we assign 60 of the remaining potatoes to the Stored at room temperature-after an hour and the remaining potatoes are assigned to the Stored refrigerated-after an hour treatment.

Part (c) step 1: Given Information

We need to describe a statistical benefit and a statistical drawback of using potatoes from only one supplier.

Part (c) step 2: Explanation

A statistical benefit of using potatoes from one supplier is that there is less variability among the potatoes since the quality of all potatoes will be similar. THis will also imply that we can more sure that the differences in the results are due to the treatment and not dues to the quality of the potatoes.

A statistical drawback is that the results of the study are only applicable to the potatoes of a single supplier and thus the results can't be generalized to all suppliers, because the different quality of the potatoes of the other suppliers could affect the effectiveness of the treatment as well.

Part (d) step 1: Given Information

We need to describe whether how they should change the design of the experiment to account for the addition of other suppliers.

Part (d) step 2: Explanation

Here,

Use a randomized block design with regular potatoes in one block and sweet potatoes in another block. Randomly assign the six treatments for each block in the same way done in part b.

Blocking by type of potatoes ensures that results are not affected by differences in potatoes type.