** This is an exercise in which you
will produce "experimental data" which will be subject to random errors
and may be subject to systematic errors. The "data" will be produced by
trimming a large rectangle to match the dimensions of a smaller target
rectangle.**

** The arrows above the large rectangle
move a vertical saw left or right, and the arrows to the left move it up
or down. The minimum size of a movement is
5 pixels. When you are satisfied with
the position of the saw, click on chop
and the cut will be made. You can trim more later but a cut cannot be undone.
[If
you find you have cut off too much, click on new
sample to reject this set of data.]
When you are satisfied with the cuts you have made, click on record
data. The width and height of your rectangle
will appear to the left of the screen with either the area or the perimeter
calculated from these dimensions.**

** Perimeter
or
Area
determines whether to display the perimeter
or the area calculated
from the recorded width and height. Both
will be included in the printout. These calculations are included
to allow comparison of the uncertainties in the calculated values to the
uncertainties in the observed values.**

** Click on new
sample to get another large rectangle to work
with. The target rectangle does not change. The target rectangle can only
be changed by changing between Practice
and Assignment modes
or by clicking on New Target.**

** The program may be operated in
Practice
or Assignment
modes:**

** In Practice
mode, the program displays statistical calculations for your measurements.
All of this data may be printed, along with details of the calculations.
The target values
may be seen after five observations have been performed. This allows
comparison of the target value to the observed mean and its standard deviation.**

** In Assignment
mode, the statistical information is not displayed. The printout is formatted
to help you perform these calculations.**

**Note: Measurements may be made either
"freehand" or by using some sort of measuring device (a notecard or a slip
of paper might be used to reproduce dimensions). Actually, it is
a good idea to do one set of five or more measurements each way.
Even with a measuring device, there will be some variation in results due
to the 5-pixel limitation, and there may be a systematic error due to parallax
or to screen distortion.**

**The statistical method (see background)
provides rules for estimating uncertainties in values calculated from experimental
measurements. This is especially important when the experimental
measurements are performed in different experiments. In this experiment,
the height and width of the target rectangle are being measured at the
same time, allowing the perimeter and/or the area of the rectangle to be
calculated for each measurement. However, this would not be possible
if one person were measuring only the width and another was measuring only
the height of the rectangle, with the results to be combined to calculate
the perimeter and/or the area. In this experiment, the perimeters/areas
from the individual observations may be averaged and uncertainties may
be calculated directly AND the heights and widths from the individual observations
may be averaged and their uncertainties calculated. This provides
a test of the rules for estimating uncertainties in calculated quantities.**

**Suggested Procedure: Have
a Calculator handy.**

**1. The program opens in PRACTICE
MODE, showing the AREA
of the cropped rectangle. Move one of the saws into position and
click on chop.
Move the other saw into position and click on chop.
Click on Record Data.**

**2. Click on New
Sample and repeat step 1 until at least five
sets of data have been recorded.**

**3. Note that the area calculated by multiplying
the mean width by the mean height is the same as the mean area.**

**
Calculate the standard deviation in the area from the standard deviations
of the width and height:**
**
s _{mean,area} = area x sqrt [ (s_{mean,width}/width)^{2}+**

**
Compare this value to the value that the program has generated by calculating
the observed areas.**

**4. At this point you may click on target
values to compare to your observations.
It is not unusual for the observed means to differ from the target values
by more than one standard deviation.**

**5. Click on t-Factors
and note the t-factor for the 95% confidence level for the number of degrees
of freedom (df) of your data.**

**6. Click on prepare
for printout, and print these results.
Note how the program has calculated standard deviations, and used the t-factor
to calculate the uncertainties at the 95% level of confidence.**

**7. Click on menu.
Remain in PRACTICE MODE
and click on Perimeter
to put the program into Perimeter Mode. The rectangles are now blue
instead of red, but the dimensions of the target rectangle has not changed.
Perform the measurements as before to generate at least five more sets
of data. If you did the first part of
this exercise without any measuring devices, use a notecard or scrap of
paper to try to improve the reproducibility of your measurements.**

**8. Note that the perimeter calculated as twice
the sum of the average width and average height is the same as the mean
perimeter.**

**
Calculate the standard deviation in the perimeter from the standard deviations
of the width and height:**

**
s _{mean,perimeter} = 2 x sqrt [ (s_{mean,width})^{2}+**

**
Compare this value to the value that the program has generated by calculating
the observed perimeters.**

**8. Click on prepare
for printout, and print these results.**

**10. Click on t-Factors
and note the t-factor for the 95% confidence level for the number of degrees
of freedom (df) of your data.**

**11. Click on prepare
for printout, and print these results.**

**12. Perform the indicated calculations.
The printouts from the PRACTICE MODE
may be used as a reference.**