The test on error analysis, Errtst, generates four questions on error analysis for you to answer. Here we describe how the test works.

You have 45 minutes to complete each attempt of the test; experience has shown that this is much more time that most students need. You may take the test four times for credit, and the mark for the test is the most recent attempt and the previous mark averaged equally. Thus, you can rapidly increase your mark. For your first attempt, you may choose to count it or not; the program will ask you after you have completed the attempt.

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:

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 ...

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.