IEEN 5321-Computer Applications of Statistical Methods Comprehensive exam part 1 Write your answers clearly and sufficiently

IEEN 5321-Computer Applications of Statistical Methods

Comprehensive exam part 1

Write your answers clearly and sufficiently.

1. (a) How many runs does a 2 7 design have? How many variables does a 2 7 design have? How many levels for each variable of a 2 7 design? (7 points)

(b) Construct a 2???????????? 5−2 design (8 points)

2. A student conducted a two-factor factorial completely randomized design. From her experiment, she has constructed the following incomplete ANOVA display: (25 points)

(a) How many levels of factor B did she use in the experiment? (2 points)

(b) How many degrees of freedom are associated with interaction? (2 points)

(c) What is the error mean square? (3 points)

(d) What is the mean square for factor A? (3 points)

(e) How many replicates of the experiment were conducted? (3 points)

(f) What are your conclusions about interaction and the two main effects? (6 points)

(g) What is an estimate of the standard deviation of the response variable? (3 points)

(h) If this experiment had been run in blocks, what would be the number of degrees of freedom for blocks? (3 points)

3. An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 23 factorial design are run. The results are as follows: (60 points)

a. Estimate the factor effects. Which effects appear to be large? (30 points)

b. Conduct the analysis of variance (????=0.05). (30 points)