9. Battery experiment, continued Suppose the battery experiment of Sect. 2.5.2 (p. 24) is to be repeated. The experiment involved four treatments, and the error standard deviation is estimated from that experiment to be about 48.66 minutes per dollar (minute/dollar).

(a) Calculate a 90% upper confidence limit for the error variance σ2.

(b) How large should the sample sizes be in the new experiment if Tukey’s method of pairwise comparisons is to be used and it is desired to obtain a set of 95% simultaneous confidence intervals of length at most 100 minutes per dollar?

(c) How large should the sample sizes be in the new experiment if Scheffé’s method is to be used to obtain a set of 95% simultaneous confidence intervals for various contrasts and if the confidence interval for the duty contrast is to be of length at most 100 minute per dollar?