Question

Lotioneer introduced a new formula for their skin lotion. They want to conduct an experiment to compare skin dryness of people using the new formula with those using the current formula

Information on the eight volunteers is shown in the table
Volunteer Gender Age, year
1 Male 23
2 Female 25
3 Female 51
4 Female 24
5 Male 22
6 Male 53
7 Male 52
8 Female 56
Part A: The scientists running the experiment think skin dryness is based on age, not gender. Create four 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 skin dryness changes based on age and gender. The firm also uses block design with four 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 the part B assigns treatments by giving treatment by giving two block the new formula and two blocks the current formula. Did they assign the treatment 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

Answer 1

To conduct a block experimental design, volunteers are grouped based on age for Part A, and on both age and gender for Part B. Assigning treatments in Part C should involve randomization to ensure unbiased distribution.

Step-by-step explanation:

To answer the student's question about comparing skin dryness using different formula lotions, we need to design an experiment using block designs.

Since the scientists believe that skin dryness is based on age and not gender, we create blocks by pairing volunteers with similar ages. Here are the four blocks:

1. Block 1: Volunteers 1 (23 years old) and 5 (22 years old)
2. Block 2: Volunteers 2 (25 years old) and 4 (24 years old)
3. Block 3: Volunteers 6 (53 years old) and 7 (52 years old)
4. Block 4: Volunteers 3 (51 years old) and 8 (56 years old)

Criteria: Volunteers are paired into blocks based on the closest ages.

The blocks will be adjusted to account for both age and gender. Here are the new blocks:

1. Block 1: Female Volunteers 2 (25 years old) and 4 (24 years old)
2. Block 2: Male Volunteers 1 (23 years old) and 5 (22 years old)
3. Block 3: Male Volunteers 6 (53 years old) and 7 (52 years old)
4. Block 4: Female Volunteers 3 (51 years old) and 8 (56 years old)

Criteria: Volunteers are paired into blocks based on the closest ages and then separated by gender.

For treatment assignment, the outside analysis firm should ensure that there is randomization within each block. A simple random selection, such as flipping a coin or drawing lots, could be used to decide which block gets the new formula and which gets the current formula. An appropriate process would be to randomly assign two blocks to the new formula and two blocks to the current formula, without any bias towards age or gender.

As such, yes, they can indeed assign the treatment appropriately using a randomized process.

Answer 2

Part A:

1 male 23

4 female 24

2 female 25

5 male 27

3 female 51

7 male 52

6 male 53

8 female 56

Part B:

4 female 24

2 female 25

1 male 23

5 male 27

3 female 51

8 female 56

7 male 52

6 male 53

Part C: The outside analysis firm did not assign the treatments properly. They should give half of each block the new formula and the other half the current formula.

Step-by-step explanation: