Question

1. the good folks at apples inc want to create bags of presliced apples for kids to easily put in their lunch boxes. they want to test different mixtures of preservatives (a, b, and c) on their honeycrisp apples. they will treat all the apples in a bushel of honeycrisps by randomly assigning them to each preservation treatment, and then comparing how long they are able to remain in the bag before they begin to brown.

a) identify the experimental units, the explanatory and response variables, and the treatments.
b) the researchers plan to use a compltely randomized desgin. describe how they should assign treatments to the 126 experimental units.
c) the researchers suspect that the type of apple will influence how well the preservation method words. they want to repeat this experiment with 4 different types of apples. describe how they should change the design of the experiment to account for this addition.

Explanation:

• a)
• Experimental units: The apples in the bushel of Honeycrisps.
• Explanatory variable: The mixtures of preservatives (A, B, and C).
• Response variable: The time until the apples begin to brown.
• Treatments: Each of the preservative mixtures (A, B, and C).
• b)
• Assign each of the 126 apples a unique number from 1 to 126.
• Use a random number generator to generate 126 random numbers.
• Sort the random numbers and assign the first 42 (if 3 treatments) to treatment A, the next 42 to treatment B, and the last 42 to treatment C.
• c)
• Use a randomized block design.
• Block the apples by type (4 types).
• Within each block (type of apple), randomly assign the apples to the 3 preservative treatments (A, B, C) as in part b.

Answer:

• a) Experimental units: Apples in the bushel of Honeycrisps. Explanatory variable: Preservative mixtures (A, B, C). Response variable: Time until browning. Treatments: Preservative mixtures (A, B, C).
• b) Assign numbers to apples, generate random numbers, sort and assign to treatments.
• c) Use a randomized block design with blocks by apple type and random assignment within blocks.