48. Suppose that in the rocket thrust problem of Exercise 43, enough resources had been available for only a half-replicate of the 24 experiment.

a. If the effect ABCD is chosen as the defining effect for the replicate and the group of eight treatments for which data is obtained includes treatment (1), what other treatments are in the observed group and what are the alias pairs?

b. Suppose the results of carrying out the experiment as described in part

(a) are as recorded here (given in standard order after deleting the half not observed). Assuming that two- and three-factor interactions are negligible, test at level .05 for the presence of main effects. Also construct a normal probability plot.

19.09 20.11 21.66 20.44 13.72 11.26 11.72 12.29