A metallurgical engineer is about to begin a comprehensive study to determine the effects of six variables on the strength of a certain type of a Hoy.
(a) If a 26 factorial design were used how many runs would be made?
(b) If a2 is the experimental error variance of an individual observation, what is the variance of a main effect'?
{c) What is the usual formula for a 99% confidence interval for the main effect of a factor?
(d) On the basis of some previous work it is believed that a-= 8000 pounds. If the experimenter wants 99% confidence intervals for the main effects and interactions whose lengths are equal to 4000 pounds (i.e., the upper limit minus the lower limit is equal to 4000 pounds), how many replications of the 26 factorial design will be required?