C'mon, guys, ease up a bit.... I'd thought it obvious that "Albert" (and/or "James Lo", and/or whoever else is using the account <[EMAIL PROTECTED]>) is a student in an introductory stats class, and that they've been introduced at least to the normal (aka Gaussian) distribution (and a table thereof) and to the Central Limit Theorem, but not yet to "Student"'s t distribution. And they have been asked to construct a confidence interval as an exercise.
Since the machinery now available to them only works if the population variance is known, the _deus_ex_machina_ (alias the textbook author, or the course instructor) has kindly provided the population mean and variance as separate information: known, as it were, full-blown from the mind (or forehead?) of Zeus. This is of course not very realistic, in that one would not in a "real" situation be likely to know these values (as several correspondents have been at pains to point out); but this is an <exercise>, and the point of an exercise is NOT to be realistic, but to provide an artificial environment in which to practice one aspect (or a few aspects) of the trade one is in the process of learning about, without having to deal with all the nasty little complications that are always lurking in the background (or even the foreground!) in "real" life. Discussion after the fact would doubtless deal with whether in fact the CI did embrace the true value of mu (that value falls rather near one edge of the CI), and therefore whether the present sample mean might be construed as having arisen from the central 95% or the extreme two-sided 5% of possible samples. On Fri, 11 Jul 2003, Rich Ulrich wrote: > On 11 Jul 2003 07:15:38 -0700, [EMAIL PROTECTED] (Jason Owen) wrote: > > > Let me get this straight -- you want to create a confidence interval > > for a mean that you *know* is equal to 53,000? Well, yes and no. I doubt that the _querent_ (Albert/James/etc.) wants to, but their _instructor_ wants them to do so. And of course for a known mean: how else can the instructor point out, afterwards, that the true mean is (or isn't) within the CI? < snip, the rest > One may note, en passant, that Albert (James, ...) made at least two errors in the calculations reported in their original post. One of those errors was subsequently acknowledged by one of them, who included a corrected computation in the later post. In my view it suffices to remark that an error occurred, and maybe give a hint as to where it occurred; to tell them what the error is would be to deprive them of the pleasure of trouble-shooting it themselves (and thereby beginning to develop some skill in trouble-shooting). ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
