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Topic: Confidence Intervals y
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Bob Hayden

Posts: 2,384
Registered: 12/6/04
Confidence Intervals y
Posted: Jan 31, 1997 10:07 PM
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----- Forwarded message from Bruce B. Richards -----

I have a question concerning confidence intervals.

1) Given a 95% confidence interval,

True or False The probability is .95 that theta falls within the
confidence interval.

2) In Siegel and Morgan_s book _Statistics and Data Analysis_ , on
page 327, under _Discussion : Interpretation of the Confidence
Interval,_ they state :

_The chances are 95% that the true population mean (theta) will be
located within the computed interval._

In your opinion are these two statements basically saying the same
thing and are they true. If you feel they are not conveying the same
idea or that they are a false statement, could you please explain why.

----- End of forwarded message from Bruce B. Richards -----

I'm not sure this distinction is worth the fuss made over it, but the
idea is that AFTER you take your sample it's a done deal and mu
(What's theta?) is either in the CI or it is not. It is sort of like
asking for the probability that the Packers win the bowl game after
the game is over. I think S&M are trying to say that before the
sample is drawn we can say that there is a 95% chance we will get a
sample whose CI includes mu. S&M generally try to be accurate, and S
knows his stuff, but I think they follow the maxim (to roughly quote
George F. Simmons) "I would rather be approximately correct and
understood than perfectly correct and incomprehensible."


_
| | Robert W. Hayden
| | Department of Mathematics
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| ) (603) 968-9914 (home)
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