Most car engines need at least 87 octane to avoid"knocking" or"pinging," terms used to describe thepre-ignition that can happen when afuel's octane is too low. An engineer is designing an experiment to raise the octane of anethanol-based fuel. From previousstudies, she thinks that with 8 experimentalruns, she will have a power of 0.90 to detect a real increase of 3 points in the mean octane. Complete partsa) andb) below.

a) If the actual increase is only 1 point and all other things remainequal, will the power be increased ordecreased? A. The power will beincreased, since the probability of incorrectly detecting the increase will be lower. B. The power will remainconstant, since the probability of incorrectly detecting the increase will remain the same. C. The power will beincreased, since the probability of correctly detecting the increase will be greater. D. The power will bedecreased, since the probability of correctly detecting the increase will be lower. E. The power will bedecreased, since the probability of incorrectly detecting the increase will be greater. F. The power will remainconstant, since the probability of correctly detecting the increase will remain the same. b) If she wants the power to be thesame, but she is interested in detecting an increase of only 1point, what will she need todo? A. She will use a smaller sample size to keep the power the same. B. She will reduce alpha while maximizing the power. C. She will redesign theexperiment, this time using a different type of fuel. D. She will use a larger sample size to keep the power the same.