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Chapter 1: Q8E (page 12)

The amount of flow through a solenoid valve in an automobile鈥檚

pollution-control system is an important characteristic. An experiment was carried out to study how flow rate depended on three factors: armature length, spring load, and bobbin depth. Two different levels (low and high) of each factor were chosen, and a single observation on flow was made for each combination oflevels.

a. The resulting data set consisted of how manyobservations?

b. Is this an enumerative or analytic study? Explainyour reasoning.

Short Answer

Expert verified

The number of observations is 8.

The study is analytic.

Step by step solution

01

Given information

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.

02

Compute the number of observations

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:

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

03

Check whether the study is enumerative or analytic

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.

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