Final answer:
For an experimental design testing three types of memory foam pillows with four different thicknesses, the manufacturer should use 12 treatment groups.
Step-by-step explanation:
The question involves determining the number of treatment groups needed for an experimental design by a pillow manufacturer who wants to test consumer opinions on different types of memory foam pillows of various thicknesses. With three types of memory foam and four different thicknesses, we use factorial design principles to calculate the total number of treatment groups required for the experiment.
To find the number of treatment groups, we multiply the number of options across each factor. The calculation would be:
Number of Memory Foam Types (3) × Number of Thicknesses (4) = Number of Treatment Groups
Calculating this gives us:
3 × 4 = 12
Therefore, the manufacturer should use 12 treatment groups in the experimental design for testing consumer opinions of pillows.