s in order to try to find the best combinations at which to operate. As an ppose the researcher is studying a certain chemical reaction and can choose four rature, five different pressures, and two different catalysts. sider all possible combinations, how many experiments would need to be ted? n preliminary experimentations, each factor is restricted to two levels. With the ctors noted, how many experiments would need to be run to cover all possible

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1. In designing an experiment, the researcher can often choose many different levels of the
various factors in order to try to find the best combinations at which to operate. As an
illustration, suppose the researcher is studying a certain chemical reaction and can choose four
levels of temperature, five different pressures, and two different catalysts.
a) To consider all possible combinations, how many experiments would need to be
conducted?
b) Often in preliminary experimentations, each factor is restricted to two levels. With the
three factors noted, how many experiments would need to be run to cover all possible
combinations with each of the three factors at two levels?
Transcribed Image Text:1. In designing an experiment, the researcher can often choose many different levels of the various factors in order to try to find the best combinations at which to operate. As an illustration, suppose the researcher is studying a certain chemical reaction and can choose four levels of temperature, five different pressures, and two different catalysts. a) To consider all possible combinations, how many experiments would need to be conducted? b) Often in preliminary experimentations, each factor is restricted to two levels. With the three factors noted, how many experiments would need to be run to cover all possible combinations with each of the three factors at two levels?
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