Re: Deriving means difference test

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
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
.

Relevant Pages

  • Re: Deriving means difference test
    ... the hypothesis found in text books for a one-tailed test is ... the book ought to give the null hypothesis as ... to zero since the null hypothesis is that mu1 and mu2 are equal. ... in the case of a one-tailed test I don't see why this second term (mu1- ...
    (sci.stat.edu)
  • Problems with textbook regarding 2 sample z-test
    ... the hypothesis found in text books for a one-tailed test is ... 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. ... I looked into several text books but none of them explains this. ...
    (sci.stat.math)
  • Deriving means difference test
    ... the hypothesis found in text books for a one-tailed test is ... to zero since the null hypothesis is that mu1 and mu2 are equal. ... in the case of a one-tailed test I don't see why this second term (mu1- ...
    (sci.stat.edu)
  • Re: Problems with textbook regarding 2 sample z-test
    ... This is probably the most basic question but I must ... second term is equal ... in the case of a one-tailed test I don't see why this ... mu2) vanishes. ...
    (sci.stat.math)
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