WHAT IT IS :: SOME SAMPLE QUESTIONS
ALTERNATIVE TO
ERRTST
As an alternative to doing the errtst again,
you may instead go through a series of exercises and answer some questions about
error analysis. We anticipate this will take you somewhat longer than getting a
good mark on errtst, and will therefore mark the assignment more leniently than
the usual U of T standard. You will be the first students to do this assignment,
and will therefore serve as "beta testers."
You may see what is involved at:
http://www.upscale.utoronto.ca/PVB/Harrison/ErrorAnalysis/index.html
If you wish to do this assignment instead of errtst, contact the author, David Harrison first. He may be reached at:
McLennan Labs, Room MP121C (North wing, first floor, South-East corner near the pay phones; 416 978 2977
What
It Is
To test your understanding of errors
you are required to take a computerized test on error analysis. You may take this test at any time that you can gain
access to a terminal to Faraday -- with the exception of those times during which regular
labs are in session. (Note that ERRTST is not available by remote-modem-login.)
If you wish credit for your mark on ERRTST, you must complete the assignment by the due date. After that date, you are free to try the exercise on the computer, but it will not be credited to your mark. The test consists of four questions to be done in 45 minutes.
You are permitted a maximum of four attempts at the test. After the first attempt, the computer will ask you if you wish the test to count in your mark. If you type " no " then the first attempt will be ignored. (This gives you a chance to become accustomed to the test.) Each attempt at the test is averaged with your previously accumulated mark to produce a new mark.
Beware!! Once you have started a test on the computer, you cannot leave the test until it is completed, i.e. once ERRTST is started a mark will always be assigned.
Note that this exercise is designed to be done as an individual effort by you. The assumptions on which ERRTST is designed are similar to other open-book tests you will encounter in university -- you are permitted to use any notes or printed material as aids in the test but you are expected to work on your own. There is normally little supervision of the test, but anyone who is found consulting others during a test will be penalized.
Some
Sample Questions
There are ten topics of error analysis that can be examined, and the
computer program chooses four of the ten at random; this means that there exist
84 different combinations of topics that you could be asked about. For each
topic, a number of versions exist, each relating that topic to a
measurement done for an existing experiment in the laboratory; the program
chooses a version at random. Then, the program randomly generates numerical data
within realistic ranges. The topics and number of versions are:
| Topic | Number of Versions |
|---|---|
| Calculating the standard deviation | 3 |
| Calculating the standard error of the mean | 3 |
| Choosing between the standard deviation and the reading error | 3 |
| Accuracy does not increase with repeated measurements | 2 |
| Propagation of errors for addition and subtraction | 3 |
| Propagation of errors for multiplication and division | 2 |
| Propagation of errors for powers | 2 |
| Propagation of errors for addition and multiplication | 2 |
| Propagation of errors for multiplication and powers | 2 |
| Rejection of measurements | 3 |
For example, for the topic of Calculating the standard deviation, the number of repeated measurements is chosen randomly to be between 4 and 8. One version randomly generates values of the time for a metal hoop to undergo 20 oscillations; the second version generates values for the thickness of a metal hoop as measured by a micrometer; the third version generates values for the width of a metal hoop as measured by a vernier caliper.
Here is a question from a particular test:
Using a vernier caliper, you have repeated measurements of the width w of a metal hoop 4 times.
You estimate that your reading error in reading the vernier is plus or minus 0.002 centimeters.
You calculate that the standard deviation of your sample of measurements is 0.001 centimeters.
What is the error, in centimeters, in each individual measurement of the width w (no units please)?
The correct answer to this question is 0.002 centimeters. If you enter that answer, the program will congratulate you and go on to the next question. If you give a wrong answer the program will state:
No. The correct answer is numerically: 0.002
This question involved the topic:
"Choosing between std. dev. and reading error"
If you wish to take some notes on this question before continuing, I have
stopped the clock.
Press RETURN to restart the clock and continue ...
N.B. Finally, the questions are such that the correct answer should have only one significant figure. The program will silently accept two significant figures, but then deducts 5% for each additional insignificant digit.
Here is another question:
You are measuring the wavelength L of a particular line in the spectra experiment using the equation:
L = [ m/(y - b) ] + L0.
You are given that L0 = 284.8 plus or minus 0.5 nm (nanometers).
The results of your calibration of your spectrometer give the slope as m = 4606 plus or minus 30 nm-units and the intercept as b = 3.82 plus or minus 0.02 units. 'units' is the units of the scale of the spectrometer.
For the particular line you are measuring, the scale on the spectrometer reads y = 15.43 units and you estimate your reading error of this scale to be plus or minus 0.02 units.
What is the error, in nm (nanometers) in your measurement of the wavelength L?
I'll leave the working out of the answer up to you!! -
A suggestion - work it out in your head first.