The statement was:
"there is a 95% chance that the true population parameter is within the computed interval."
One reply was:
Here's a counter argument, courtesy of Freedman, Pisani, and Purves, Statistics, 3rd ed., p. 384:I would suggest, by the way, that (applying this level of pedantic correctness consistently) we should not describe a vague statement that permits either a correct or incorrect reading as "absolutely not true."
"It seems more natural to say 'There is a 95% chance that the population percentage is between 75% and 83%.' But there is a problem here. In the frequency theory, a chance represents the percentage of the time that something will happen. No matter how many times you take stock of all the students registered at that university in the fall of 1994, the percentage who were living at home back then will not change. Either the percentage was between 75% and 83%, or not. There really is no way to define the chance that the parameter will be in the interval from 75% to 83%. That is why statisticians have to turn the problem around slightly. They realize that the chances are in the sampling procedure, not in the parameter. And they use the new word "confidence" to remind you of this." [Footnote omitted.]
I like that explanation. It forces you to remember "that the chances are in the sampling procedure, not in the parameter." It means that a teacher who corrects a student for saying "there's a 95% chance that the parameter is in this interval" is not being pedantic. The teacher is trying to get it exactly right and showing the student that wording matters. The student may know the parameter is fixed, but then again, maybe not . . .
Prof. Humberto Barreto
Department of Economics
Wabash College
Crawfordsville, IN 47933
[EMAIL PROTECTED]
Voice: (765) 361-6315
FAX: (765) 361-6277
http://www.wabash.edu/econexcel
.
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