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

Part A:

Creation of four blocks of two volunteers:

PART A: Skin Dryness based on age:

Volunteer     Gender     Age, year

5                     Male         22

1                      Male         23

4                     Female     24

2                     Female     25

3                     Female     51

7                     Male         52

The criteria for creating the blocks is age.  The gender is not a material consideration.

Part B:

Creation of four blocks of two volunteers:

PART B:  Skin Dryness based on Age and Gender:

Volunteer     Gender     Age, year

5                     Male         22

4                     Female     24  

1                      Male         23

2                     Female     25

3                     Female     51

6                     Male        53

7                     Male         52

8                     Female    56

The criteria for creating the four blocks are age and gender.  Each gender is included in each group.

Part C:

Randomly assigning treatment to groups without regard to their group dynamics may not be the most efficient.  The new treatment formula should be assigned to one of the young groups and one of the old groups, using stratification.  This will help to explain if age or gender causes skin dryness or not.

Step-by-step explanation:

a) Data and Calculations:

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: Skin Dryness based on Age:

Volunteer     Gender     Age, year

5                     Male         22

1                      Male         23

4                     Female     24

2                     Female     25

3                     Female     51

7                     Male         52

6                     Male        53

8                     Female    56

PART B:  Skin Dryness based on Age and Gender:

Volunteer     Gender     Age, year

5                     Male         22

4                     Female     24  

1                      Male         23

2                     Female     25

3                     Female     51

6                     Male        53

7                     Male         52

8                     Female    56

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.