Problem 1: How well can you control your watch? Your supervisor at the Highway D

Question

Problem 1: How well can you control your watch? Your supervisor at the Highway Department Research Station needs to know about the accuracy of time measurements your group can make with a stopwatch. The watch may produce numbers showing tenths or even hundredths of a second, but it is ridiculous to suppose that your measurements can be accurate to within such a small margin of error ine an experiment where you start the watch and then, while staring at the watch face, you try to stop the watch at exactly the 10 second mark. Of course, your reactions are not good enough to do this within 1/100 of a second, at least all the time. What you are actually measuring is how well you can control the watch. Thus, you will get a statistical distribution of measurements from which you can estimate the rms variability. This is what limits the accuracy in a time measurement. 2-4

Explanation / Answer

In order to cover the 2/3 of the data we must cover +- 1 SD of the data , as we know that about 68% of the data is covered within +- 1 SD , so lets calculate the SD of the error

error <- c(-0.71,0.2,-0.66,-0.52,0.26,-0.02,-0.15,0.13,0.32,0.29,0.2,-0.14)
sd(error)

we see that SD is 0.375

hence the interval would be

-0.375 to 0.375

also , 0.36 is covered in the interval -0.375 to 0.375

This means that the average term is within the interval calculated

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