Deriving means difference test
- From: "Bob" <frotty22@xxxxxxxxx>
- Date: 19 Feb 2007 13:09:37 -0800
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.
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
.
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