Bob wrote:
Hi,
This is probably the most basic question but I must be missing
something: I am looking at a test of 2 independent samples where the
means are assumed to be normally distributed and I want to do a z-
test. Now there are 2 things which confuse me:
First, the hypothesis found in text books for a one-tailed test is
often
H0: mu=100
H1: mu<100
Why does it not say H0: mu>=100? There is only one area of rejection
on the left tail of the distribution.
For a directional test, the book ought to give the null hypothesis as
you've shown it.
Second, when I try to derive the z-test statistic to compute the
critical value, I take (xbar1-xbar2)-(mu1-mu2) in the numerator. For a
two-tailed test I get the usual formula where the second term is equal
to zero since the null hypothesis is that mu1 and mu2 are equal. But
in the case of a one-tailed test I don't see why this second term (mu1-
mu2) vanishes.
Can somebody clarify this for me? I looked into several text books but
none of them explains this.
Thanks a lot!
Bob
Think of mu=100 as the worst case for the null hypothesis. If you can
reject H0 with mu = 100, you will also reject it for any mu > 100. So
even though H0 states that mu>=100, you use mu=100 for testing.
--
Bruce Weaver
bwea...@lakeheadu.cawww.angelfire.com/wv/bwhomedir
