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 are the potatoes used in the experiment. The explanatory variables are storage time and time from slicing until cooking. There are six treatments: fresh picked and cooked immediately, fresh picked and cooked after an hour, stored at room temperature and cooked after an hour, stored at room temperature and cooked immediately, stored in refrigerator and cooked immediately and stored in refrigerator and cooked after an hour. The response variables are ratings of colour and flavour.

b. The remaining $50$potatoes are assigned to treatment$6.$

c. The result will not be accurate.

d. Blocking by type of potato ensures that results are not affected by differences potato type.

Step-by-step solution

Part a. Step 1. Explanation

Experimental units can include things like people, animals, or objects.

The explanatory variable is the one that is changed in order to see the effect on the response variable.

The experimental units are the potatoes used in the experiment. The explanatory variables are storage time and time from slicing until cooking. There are six treatments: fresh picked and cooked immediately, fresh picked and cooked after an hour, stored at room temperature and cooked after an hour, stored at room temperature and cooked immediately, stored in refrigerator and cooked immediately and stored in refrigerator and cooked after an hour. The response variables are ratings of colour and flavour.

Part b. Step 1. Explanation

In part (a), we determine that there were six treatments and thus we should assign $\frac{300}{6}=50$potatoes to each treatment.

Let us assign a unique number between $1and300$to each potato.

Use slips of paper, a random digit table or a calculator to select $50.$

Unique integer between $1and300$. The corresponding $50$potatoes are then assigned to treatment $1.$

Similarly, we will assign $50$unique potatoes to treatment $2,3,4and5$while make sure that no potatoes were already assigned to a previous treatment.

Finally, the remaining $50$potatoes are assigned to treatment$6.$

Part c. Step 1. Explanation

The statistical benefit of using potatoes from only one supplier is that the sample size will be small and it will not be complex. The time will be saved and it can be give the result quickly. The statistical drawback of using potatoes from only one supplier is that it will give the bias result as it will not represent the whole population. Thus, the result will not be accurate.

Part d. Step 1. Explanation

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 potato ensures that results are not affected by differences potato type.