matt wrote in sci.stat.edu:
>hi, I need some help with this question
>A 95% confidence interval was found for the difference in mean family
>annual income, between an outer suburb and a rural townn. Use this CI
>to carryout a test of Ho: Us=Ur+25 against Ho: Us#Ur+25, ie that
>suburb incomes are $25,000 per annum greater than rural incomes. use
>the six steps solution
I don't know what "the six-step solution" is, but the steps are
presumably listed, numbered, in your textbook somewhere. I assume
they are the same steps of hypothesis testing that we all know, just
arranged in the author's preferred way.
Now _if_ your alternative hypothesis is truly =/= (rather than >,
which might seem more reasonable to test), then you have a two-
tailed test. The critical points of a two-tailed hypothesis test
with alpha = 0.05 correspond exactly to the endpoints of the 95%
confidence interval, because 0.05 + 95% = 1. If you are quoting the
problem correctly, you are instructed to use this fact instead of
carrying out a hypothesis test in the regular way. (Again, I don't
know how "six steps" figures into this.)
>95% CI for mu rural - mu suburb: ( -39366, -29109)
(I think it would have been slightly cleaner to calculate the CI for
suburb - rural, but as long as you're careful with signs you can do
it either way.)
Therefore, assuming you have calculated your confidence interval
correctly (I didn't check), then there is no need to compute a t
statistic: you simply look at whether the hypothesized difference is
inside the confidence interval or outside it. The hypothetical
difference is mu_s = mu_r + 25000 or mu_r - mu_s = -25000. That
figure is outside the confidence interval, and therefore you would
reject the null hypothesis and accept the alternative.
Don't get too excited about using CI to perform HT. This works only
when the confidence level complements the significance level.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com/
"You despise me, don't you?"
"If I gave you any thought, I probably would."
-- Casablanca
.
.
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