Most car engines need at least 87 octane to avoid"knocking" or"pinging," terms used to describe the pre-ignition that can happen when a fuel's octane...

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

a) If the actual increase is only 1 point and all other things remain equal, will the power be increased or decreased?

A. The power will remain constant, since the probability of correctly detecting the increased will remain the same.

B. The power will reman constant, since the probability of incorrectly detecting the increased will remain the same.

C. The power will be increased, since the probability of incorrectly detecting the increased will be lower.

D. The power will be increased, since the probability of incorrectly detecting the increased will be greater.

E. The power will be decreased, since the probability of incorrectly detecting the increased will be greater.

F. The power will be decreased, since the probability of incorrectly detecting the increased will be lower. 

b) If she wants the power to be the same,  but she is interested in detecting an increase of only 1 point, what will she need to do?

A. She will use a larger sample size to keep the power the same

B. She will redesign the experiment, this time using a different type of fuel

C. She will reduce alpha while maximizing the power

D. She will use a smaller sample size to keep the power the same