Chapter 4, Problem R4.6RE

(a)

To determine

To identify the experimental units, the factors, the number of levels for each factor and the treatments.

Answer to Problem R4.6RE

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.

Explanation of Solution

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.

(b)

To determine

To describe a completely randomized design for this experiment using $300$ potatoes.

Explanation of Solution

Given: $300$ potatoes.

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

  $\begin{array}{l}\text{Let us assign a unique number between 1 and 300 to each potato}\text{.}\\ \text{Use slips of paper, a random digit table or a calculator to select 50}\\ \text{unique integers between 1 and 300}\text{. The corresponding 50 potatoes are then assigned}\\ \text{to treatment 1}\text{.}\\ \text{Similarly, we will assign 50 unique potatoes to treatment 2,3,4 and 5}\\ \text{while make sure that no potatoes were already assigned to a previous treatment}\text{.}\\ \text{Finally, the remaining 50 potatoes are assigned to treatment 6}\text{.}\end{array}$

(c)

To determine

To describe a statistical benefit and a statistical drawback of using potatoes from only one supplier.

Explanation of Solution

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.

(d)

To determine

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

Explanation of Solution

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.