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a. There are 12 observations from the resulting data set.

b. This is an analytic study.  It compares the flow rates through a solenoid valve based on three factors at four different levels.

Step-by-step explanation:

Observations of the dependence of flow rate

Factors              Armature    Spring    Bobbin

                           Lengths      Load      Depth

Levels

Low                          1                1               1

Moderate                 1                1               1

High                         1                1               1

Extreme                   1                1               1

Total observations  4               4              4

Number of observations = 12

b) Whereas enumerative studies are statistical studies carried out to draw a conclusion on a process or a condition, analytic studies are statistical studies that compare two or more groups or sets of data to improve future performance.  The focus of an analytic study is on the process rather than the condition.  Enumerative studies tend to explain, evaluate, and describe the condition of the dataset.