Home Work 6
1 Scientists ran two replicates of a 22design to determine the effect of kind
of ignitor and type of main charge of the delay time of a fuse. They
definitely want to keep the delay time under 30 seconds. The results of
the experiment were
Rep. 1 Rep. 2
Ignitor Main Charge Delay Delay
1 1 10.70 9.82
2 1 18.42 18.62
1 2 15.04 16.02
2 2 22.94 31.22
(a) Draw a box and attach the sample means at the corners.
(b) Estimate the main effect of Ignitor, main effect of Charge and their
interaction. Base your calculations on your figure in Part(a).
(c) Calculate 95 % confidence intervals for your estimates in Part (b).
Interpret the results.
(d) Write the design with three columns of ±1 and calculate the esti-
mated effects using this column and the column of means.
2 The experiment in Problem 1 was actually part of a larger experiment
that involved two different booster charges, one powder and one pellet.
Rep. 1 Rep. 2
Ignitor Main Charge Booster Delay Delay
1 1 powder 10.70 9.82
2 1 powder 18.42 18.62
1 2 powder 15.04 16.02
2 2 powder 22.94 31.22
1 1 pellet 10.02 10.36
2 1 pellet 22.80 25.14
1 2 pellet 27.26 21.42
2 2 pellet 32.92 21.38
(a) Draw a cube and attach the sample means at the corners.
(b) Estimate the the main effects, the three two factor interactions and
the three factor interaction. Base your calculations on your figure in
Part(a).
(c) Calculate 95 % confidence intervals for your estimates in Part (b).
(d) Write the design with seven columns of ±1 and calculate the esti-
mated effects using this column and the column of means.
3 Check your answers to problems 1. and 2. Comment on any differences.
How do the sums of squares for any factor compare with estimated effect
in each case?
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