(03.02, 03.04 MC) Sudzy introduced a new formula for their hair conditioner. They want to conduct an experiment to compare the hair strength of people using the new formula with those using the current formula. Information on the twelve volunteers is shown in the table.

Volunteer Gender Age, year
1 Male 21
2 Female 37
3 Female 30
4 Male 32
5 Male 24
6 Female 22
7 Male 45
8 Female 42
9 Male 42
10 Female 47
11 Male 36
12 Female 23
Part A: The scientists running the experiment think hair strength changes based on age, not their gender. Create six blocks of two volunteers and identify the volunteers, by number, who would be included in each block. Explain the criteria you used to create the blocks. (3 points)

Part B: The company brings in an outside analysis firm that believes hair strength changes based on age and gender. The firm also uses block design with six blocks of two volunteers for each block. Group the volunteers, by number, who would be included in each block. Explain the criteria you used to create the blocks. (3 points)

Part C: The outside analysis firm from part B assigns treatments by giving three blocks the new formula and three blocks the current formula. Did they assign the treatments appropriately? If so, explain a suitable process for selecting the blocks that receive the new formula. If not, explain a suitable method for assigning treatments. (4 points)

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