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FACULTAD DE CIENCIAS QUMICAS MAESTRA EN CIENCIAS QUMICAS

EXAMEN DE DISEO DE EXPERIMENTOS (MDULO II) SEMESTRE AGOSTO DICIEMBRE DE 2014

Instrucciones:

a) Los problemas aqu planteados son para resolverse en casa y la metodologa seguida para su resolucin deber exponerse y explicarse mediante una presentacin PowerPoint.

b) Para la resolucin de los problemas diseo de experimentos y ANOVA use el software Design Expert o Minitab.

c) La entrega de los archivos y presentacin se har el da y a la hora sealada por el Maestro del curso.

d) Firme con su palabra de honor: Certifico que el trabajo desarrollado en este examen es mi propio trabajo.

Nombre y Firma: 1. Resuelva los problemas 3.11, 7.6 y 7.7 del Libro Estadstica y Quimiometra para Qumica

Analtica Autor: Miller & Miller, 4th. Edicin, 2002.

2. An article in Industrial Quality Control (1956, pp. 5-8) describes an experiment to investigate the

effect of the type of glass and the type of phosphor on the brightness of a television tube. The response variable is the current necessary (in microamps) to obtain a specified brightness level. The data are as follows:

(a) Is there any indication that either factor influences brightness? Use = 0.05

(b) Do the two factors interact? Use = 0.05.

(c) Analyze the residuals from this experiment.

3. As part of an investigation of toxic agents and antitoxins, 4 rats were subjet the same deadly poison. Then they treated with a mixture of two antotoxins. They were allocated 2 concentrations of antitoxin I: 10% and 20% and 2 concentrations of antitoxin II: 0.5% and 1%. The response was survival time in tens of hours. The experiment result in the following data.

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Task 1. What kind of design do we deal here? What is its purpose?

Task 2. Perform analysis of variance, estimate the factor effects and construct a normal probability plot of the effect estimates. Explain the plots.

Task 3. Get response surface graphs and explain them.

Task 4. There is some evidence indicating an interaction between the factors? (Use =0.05).

Task 5. Is the model significant?

4. Assume that an experiment is to be conducted to examine the effect of four different gasoline additives A, B, C, and D on reduction of nitrogen oxides. Four cars are available for the experiment, as are four drivers. Assume that differences are expected between the cars and between the drivers, so these are to serve as blocking factors.

a) How would you design the experiment if 16 runs were to be made, assuming an identical driving course (terrain)?

b) Now assume that because of time considerations, it isnt practical to use the same driving course for each run, as that would require various combinations of cars and drivers to be constantly in waiting, so this would not be an efficient use of resources. To alleviate this problem, four driving courses (routes) are laid out. Now explain how the experiment should be designed and performed.

c) Considering the number of observations, would you suggest that the design that you named in part (b) be replicated? If so, how would the replication be performed?

5. True/False

a) In an experiment, the variable that is observed or controlled for the purpose of determining its effect on the value of another variable is called the dependent variable.

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b) For an experiment associated with analysis of variance, the independent variable(s) can be either qualitative or quantitative.

c) When there is only one factor in an ANOVA design, it is appropriate to refer to each factor level as a treatment.

d) One-way ANOVA assumes that the samples have come from populations that have equal variances.

e) In the randomized block design, the purpose of the blocking variable is to reduce the amount of error variation.

6. Explain the difference between a 23 design and a 32 design.

7. Complete la siguiente tabla de anlisis de varianza, concluya e interprete. Se midi el rendimiento de trigo (kg/parcela) cuando se aplicaron 4 tipos de fertilizantes (tratamientos).