Emily,

Thank you for asking. The LRT critical value given in the notes has a typo – the “2” should be removed so that only 1-alpha is present. Fortunately, the correct critical value is given on p. 35 of the book.

Chris

**From:** STAT 875 Listserv <[log in to unmask]> **
On Behalf Of **Emily Robinson

**Sent:** Wednesday, February 13, 2019 11:31 AM

**To:** [log in to unmask]

**Subject:** Re: Exam #1 Question

Hello,

While studying, I came across a question regarding the critical value for the Pearson chi-square test (pg. 1.66) and the LRT (pg. 1.68) for the hypothesis test, testing H0: pi1 – pi2 = 0 vs Ha: pi1 – pi2 ne 0. The Pearson chi-square critical
value is chi-square (1, 1 – alpha) while the LRT critical value is chi-square (1, 1 – alpha/2). Why does it appear the Pearson is conducting a one sided test while the LRT appears to be conducting a two sided test?

Thank you!

Emily