Accept inexact answers for area computations using z-scores. #31164

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saasmath commented Oct 2, 2012

In math and statistics courses, many students are taught to use graphing calculators or other
technology, rather than tables, to compute areas under the normal curve. These will differ
in the last digit frequently from the approximate z-tables, leading to incorrectly reported errors in
the exercises.
This fixes the issue by accepting the correctly rounded technology produced answer.

Gary Anderson
Accept inexact answers for area computations using z-scores.
In math and statistics courses, many students are taught to use graphing calculators or other
technology, rather than tables, to compute areas under the normal curve.  These will differ
in the last digit frequently from the approximate z-tables, leading to incorrectly reported errors in
the exercises.
This fixes the issue by accepting the correctly rounded technology produced answer.
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We make it pretty obvious that you're supposed to be using the table given below, and I think that if you're getting different answers you probably did some rounding incorrectly (I assume we calculated our z-score grid correctly). However, I wouldn't be opposed to this, if others think it's helpful.

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xymostech commented Oct 2, 2012

We make it pretty obvious that you're supposed to be using the table given below, and I think that if you're getting different answers you probably did some rounding incorrectly (I assume we calculated our z-score grid correctly). However, I wouldn't be opposed to this, if others think it's helpful.

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saasmath Oct 3, 2012

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I'm not sure it is obvious to students that a z-table is the only appropriate way to answer this question, or whether it is just one suggested approach, and in my experience it leads to confusion to count calculator generated responses as incorrect. One has to decide if the goal of this exercise is to teach z-table reading to the exclusion of other commonly taught approaches, or instead practice finding the area under a normal curve using any technique. As a teacher, I assign these exercises for the second reason.

To show that this is not a rounding issue, consider z-scores_3, seed #68. Lower limit 78, upper limit 83, mean 80, SD 5. The area under the curve to 10 decimal places is .3811686325. Correctly rounded to the hundredth place and expressed as a percentage (as the exercise expects), one would enter 38.12%. Using the table, one gets an answer 38.11% and is counted wrong when they enter the more accurate, calculator produced, answer.

Some teachers and professors will use tables for logs, trig values, and even teach students to use slide rules. In my view, these exercises should be agnostic as to technology.

This patch does not prevent one from using the table, but does make the exercise useful in those cases where 4-digit tables are not the chosen technology for solving this family of questions.

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saasmath commented Oct 3, 2012

I'm not sure it is obvious to students that a z-table is the only appropriate way to answer this question, or whether it is just one suggested approach, and in my experience it leads to confusion to count calculator generated responses as incorrect. One has to decide if the goal of this exercise is to teach z-table reading to the exclusion of other commonly taught approaches, or instead practice finding the area under a normal curve using any technique. As a teacher, I assign these exercises for the second reason.

To show that this is not a rounding issue, consider z-scores_3, seed #68. Lower limit 78, upper limit 83, mean 80, SD 5. The area under the curve to 10 decimal places is .3811686325. Correctly rounded to the hundredth place and expressed as a percentage (as the exercise expects), one would enter 38.12%. Using the table, one gets an answer 38.11% and is counted wrong when they enter the more accurate, calculator produced, answer.

Some teachers and professors will use tables for logs, trig values, and even teach students to use slide rules. In my view, these exercises should be agnostic as to technology.

This patch does not prevent one from using the table, but does make the exercise useful in those cases where 4-digit tables are not the chosen technology for solving this family of questions.

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Opps, only the original commit was intended to be part of this pull request. In the future I won't push the master branch.

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saasmath commented Oct 3, 2012

Opps, only the original commit was intended to be part of this pull request. In the future I won't push the master branch.

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Okay, this seems reasonable to me. Do you know how to use git well enough to get rid of the "Merge branch 'master'" commit, so we don't have that in our commit history?

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xymostech commented Oct 3, 2012

Okay, this seems reasonable to me. Do you know how to use git well enough to get rid of the "Merge branch 'master'" commit, so we don't have that in our commit history?

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No, if you can give me the git commands to get rid of "Merge branch master" and the other commit I would be happy to do that before integration. The decimal answer for computing means should have a separate discussion.

It seems like this involves pushing a rebase, but I am not good enough at git yet to do this correctly.

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saasmath commented Oct 3, 2012

No, if you can give me the git commands to get rid of "Merge branch master" and the other commit I would be happy to do that before integration. The decimal answer for computing means should have a separate discussion.

It seems like this involves pushing a rebase, but I am not good enough at git yet to do this correctly.

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Lemme try squashing the commits...

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beneater commented Oct 3, 2012

Lemme try squashing the commits...

@beneater beneater closed this in 5c60a28 Oct 3, 2012

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success!

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beneater commented Oct 3, 2012

success!

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