[ww-bugs] Bug 4100: New: inconsistency using tables/exact values

[bugzilla-daemon at webwork.maa.org]

http://bugs.webwork.maa.org/show_bug.cgi?id=4100

           Summary: inconsistency using tables/exact values
           Product: Problem Libraries
           Version: unspecified
          Platform: PC
               URL: /opt/webwork/courses/MATH2441/templates/Library/Colleg
                    eOfIdaho/setStatistics_Ch19InferencePropn/19Stats_07_I
                    nferencePropn.pg_with_problemSeed=1234
        OS/Version: Linux
            Status: NEW
          Severity: normal
          Priority: P5
         Component: Library (OPL)
        AssignedTo: gjennings at csudh.edu
        ReportedBy: wub7quxa at gmail.com
        Web browser Firefox
           version:


The idea here is to calculate the sample size $n$ given the desired margin of
error $E$ and the confidence level $z_{\frac{\alpha}{2}}$ (I will call it $z$
for short). The formula is 
\[
E=\frac{z_{\frac{\alpha}{2}}^{2}\cdot{}0.25}{E^{2}}
\]
Here is the problem: the author uses 2.576 for $z$ calculating the answer. In
the instructions, the author states: "use the values for z* from a z-table" -->
all the tables that I know provide 2.575 rather than 2.576. The more exact
value is 2.575829, so the author is correct in some sense. However, the tables
are usually precise only to two digits after the decimal point, and the only
reason 2.575 is used is because the p-value for 2.57 is 0.9949 and the p-value
for 2.58 is 0.9951. Students would correctly take the mean of 2.57 and 2.58 to
use in this problem, which is 2.575, not 2.576.

I suggest that a tolerance level is introduced for this problem so that all
three alternatives, 2.575, 2.576, and 2.575829, give the correct answer.
Currently, 2.575 gives an incorrect answer.

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