AP Statistics question

Test Preparation AP Test Preparation
1

<p>So I’m using CliffsAP for practice testing, and I came across this question that I believe had an error in the answer. I’ve come across a couple errors before, but I am not very good at this type of conceptual stuff so I want to make sure the book is wrong: </p>

<p>An automotive company wants to estimate the mean life span of their auto batteries. After sampling 79 batteries, a 95% confidence interval was computed to be [289 hours, 297 hours]. However, the sample of battery life spans contained one extremely low value. If this low value is removed from the sample and the interval is recomputed, which of the following will be true?
I- The width of the interval will be decreased.
II- The center of the interval will be decreased.
III- The error of the interval will be decreased.</p>

<p>I know I and III are true, and the book confirmed these, but the book says II is true as well. However, wouldn’t the center increase since you remove a very low value?
Please either confirm that the book is wrong, or if it is right about #II please explain.</p>

2

<p>I would assume that the book is wrong. The center of a confidence interval is the sample mean. Means are not resistant to outliers, so a low number would decrease the mean. Removing a low number would raise the mean. Proof: Take the average of 80, 100, and 0. It’s 60. Remove the 0: the new mean is 90, which is an increase from 60.</p>