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A study was conducted on how flow rate depended on three factors; armature length, spring load, and bobbin depth.

Two levels of each factor were selected and a single observation on flow was made for each combination of levels.

a.

Consider L and H represents low and high levels for each factor. The three factors are Armature as A, Spring load as S and Bobbin depth as B.

Since the number of factors is 3 and the number of levels is 2.

The total number of observations is computed as,

\(\begin{array}{c}{\rm{Number of observations}} &=& 2*2*2\\ &=& 8\end{array}\)

Therefore, the number of observations is 8.

The 8 possible observations are:

\(\left\{ \begin{array}{l}\left( {{L_A},{L_S},{L_B}} \right),\left( {{L_A},{L_S},{H_B}} \right),\left( {{L_A},{H_S},{L_B}} \right),\left( {{H_A},{L_S},{L_B}} \right),\\\left( {{L_A},{H_S},{H_B}} \right),\left( {{H_A},{L_S},{H_B}} \right),\left( {{H_A},{H_S},{L_B}} \right),\left( {{H_A},{H_S},{H_B}} \right)\end{array} \right\}\)

An enumerative study is a study where the population is finite whereas an analytic study is a study where the population from which a sample is drawn is nonidentifiable.

The provided study is an analytic study as the study analyses the amount of flow through solenoid valve in an automobiles pollution control system. The provided study is conducted to get the information from the existing process.

Therefore, there is no sampling frame.