Avirologist has asked you to design an experiment to compare the effects of two different media (a and b) and two different incubation times (12 and 18 hours) on the growth of a specific bacteria. she has access and money to do 24 different runs (single combination of the two factors like media a for 12 hours) but can only do as many as 6 runs a day. (a) based on this information, propose two potential balanced designs that use all 24 runs and present an anova table with sources and degrees of freedom. (b) suppose the experimenter wants to minimize the length of a 95% confidence interval for a treatment difference (mi - hi). which of the two designs proposed in (a) is better? explain.