Question

There is a total of 6 trials for an experiment involving the measurement of standard enthalpies (kcal/mol).

a) If additional data points are taken but the standard deviation and mean remain unchanged, what will happen to the 95% confidence interval? Would it increase, decrease, or stay the same?

b) What are the different ways to identify a systematic error in her data for this experiment ?

Answer 1

a) the formula for confidence level is: xt s/(n)^1/2 we already know that the sample "n" is increasing. and all the other data remains the same, so, increasing the value of n, means that the value of n^1/2 in the above expression will be higher. So when the division of the above data with the increase value of n is done, the confidence level will decrease (You are dividing for example 10 / 3 instead of 10 / 2) so, that's why the confidence intervall will decrease as the sample size is increased.

b)

Systematic error can be located and minimized with careful analysis and design of the test conditions and procedure; by comparing your results to other results obtained independently, using different equipment or techniques; or by trying out an experimental procedure on a known reference value, and adjusting the procedure until the desired result is obtained (this is called calibration). A few items to consider:

1. What are the characteristics of your test equipment, and of the item you are testing? Under what conditions will the instrument distort or change the physical quantity you are trying to measure? For example, a voltmeter seems straightforward enough. You hook it up to two points in a circuit and it gives you the voltage between them. Under conditions of very low current or high voltage, however, the voltmeter itself becomes a significant part of the circuit, and the measured voltage may be significantly altered. Similarly, a large temperature probe touched to a small object may significantly affect its temperature, and distort the reading.
2. Check that any equations or computer programs you are using to process data behave in the way you expect. Sometimes it is wise to try a program out on a set of values for which the correct results are known in advance, much like the calibration of equipment described below.
3. It is unusual to make a direct measurement of the quantity you are interested in. Most often, you will be making measurements of a related physical quantity, often several times removed, and at each stage some kind of assumption must be made about the relationship between the data you obtain and the quantity you are actually trying to measure. Sometimes this is a straightforward conversion process; other cases may be more subtle. For example, gluing on a strain gauge is a common way to measure the strain (amount of stretch) in a machine part. However, a typical strain gauge gives the average strain along one axis in one particular small area. If it is installed at an angle to the actual strain, or if there is significant strain along more than one axis, the reading from the gauge can be misleading unless properly interpreted.
4. Calibration: Sometimes systematic error can be tracked down by comparing the results of your experiment to someone else's results, or to results from a theoretical model. However, it may not be clear which of the sets of data is accurate. Calibration, when feasible, is the most reliable way to reduce systematic errors. To calibrate your experimental procedure, you perform it upon a reference quantity for which the correct result is already known. When possible, calibrate the whole apparatus and procedure in one test, on a known quantity similar in size and type to your unknown quantities.

Hope this helps