Your English is better than that of many of my born-in-USA students;-) I work regularly with high school teachers of AP Statistics -- a program that allows high school students to get college credit for college courses taken in high school -- in this case, an introductory statistics course. If I understand you then this is a question that comes up regularly in AP Stats. (where the students use graphing calculators with many statistical functions).
Should we work with the given units and technology that has normal tables for any mu and sigma OR should we standardize everything? When we have the option, using the given units seems more natural. OTOH, standardizing provides review and practice of an important idea. In addition, if we introduce the t distrtibutin later, we will have to do a kind of standardization there, so doing things different ways in different chapters hides the essential difference behind a surface difference. If we standardize in both cases students see that the difference is whether we know sigma, not whether we standarize or not. ----- Forwarded message from David Monterde <[email protected]> ----- Date: Thu, 20 Apr 2017 17:07:45 +0200 From: David Monterde <[email protected]> To: [email protected] Subject: [R-sig-teaching] About the standard gaussian distribution X-Mailer: iPhone Mail (14E304) First of all I have to apologize because my english is horrible. I am working in a basic and practical statistic course. I will speak about confidence intervals, of course. But when I was preparing this chapter I had a doubt: I wonder if it has sence today to explain the confidence intervals for a mean in terms of the standard normal distribution. If we show that the mean follows a normal distribution with variance/n then it is easy to explain (and to understand) that the confidence interval is due to two percentiles, the percentile alpha/2 and the percentile 1-alpha/2 from a normal distribution with the sample mean and the sample variance/n. I think that the standard gaussian distribution was usefull when we had to calculate CI in the past. That is, it was a simple way to have all possibilities in a single table (in paper). But now, we have R functions that let us to obtain the exact values for any normal distribution. I think that is not necessary to explain how to work with transformations if we can explain that a CI is simply to identify percentiles. What do you think? Thanks PD I know that the normal distribution for CI need some hipothesis. But I have focused the question _________________________ David Monterde Lo dif??cil se hace. Lo imposible se intenta. _________________________ [[alternative HTML version deleted]] _______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-teaching ----- End forwarded message ----- -- -------> First-time AP Stats. teacher? Help is on the way! See http://courses.ncssm.edu/math/Stat_Inst/Stats2007/Bob%20Hayden/Relief.html _ | | Robert W. Hayden | | 5 Howard Street, Apartment 206 / | Wilton, New Hampshire 03086 USA | | | | email: bob@ the site below / x | website: http://statland.org | / '''''' _______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-teaching
