a statistic-teaching question
I hypothesize that the person who wrote question (1) expects the student to compute the sample mean (71.55) and se (2.06), assume that the sample mean is normally distributed with that mean and sd, and compute Pr(X >72.5|mu=71.5,sigma=2.06), ie about .32. Since frequentists don't have probability distributions for parameters, that would be nonsense, or as some already stated, the answer is 0 or 1, and we don't know which. The question clearly does not assume a prior, so a Bayesian interpretation would presumably be out of order. question (2) exhibits the same confusion. albyn
On Tue, Jul 13, 2010 at 06:21:50AM -0700, jose romero wrote:
Dear R-teaching list: I would like to put forward for your consideration an issue which is not R related, but statistics-teaching related.? Although i know full well that this list is intended for discussion of the use of R in teaching statistics, I also know that most (if not all) of you out there are highly qualified statistics teachers, and as such, I'd like to know your opinion on this issue: As a statistics instructor in a open university (distance education), part of my job functions consist in grading exams written at the central level in my institution and presented by students nationwide.? Recently, i had to grade an exam of which the first two questions ran like this (again, i did not write this exam): 1) The following is a sample of the duration (in minutes) of time intervals between queries to a data base: ??? 91??? 86??? 71??? 79??? 51??? 51??? 67??? 60??? 79??? 85 ??? 68??? 86??? 53??? 45??? 86??? 71??? 82??? 88??? 72??? 67 ??? 51??? 51??? 75??? 81??? 76??? 80??? 75??? 76??? 82??? 49 ??? 66??? 83??? 84??? 82??? 84??? 76??? 53??? 75??? 70??? 55 What is the probability that the mean time between queries is more than 72.5 minutes? 2) For a certain region of the country, the rainfall measurements (in mm) during the last 15 years are the following: ??? 580??? 575??? 400??? 750??? 428??? 636??? 825??? 360 ??? 850??? 590??? 875??? 735??? 920??? 950??? 550 What is the probability that the average rainfall during the last 15 years is less than 625 mm? Considering that these are exam questions for an introductory statistical inference course (non bayesian), what are your objections, as a teacher, to the way these questions are posed?? If you had to grade exams with such questions, and it is not in your power to cancel this exam and re-schedule for another one, how would you grade your pupils?? Once again, please excuse me for posting these non-R related and very absurd questions for your consideration.? However, i'd really like to know the experts' opinion on this. Thanks in advance, jos? romero [[alternative HTML version deleted]]
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Albyn Jones Reed College jones at reed.edu