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## 'Reaction Timer Timer' printed from http://nrich.maths.org/

This problem gives students a real statistical challenge to
address. It can be accessed at various levels and includes issues
of measurement, sampling and hypothesis testing. At the highest
level, students can create a hypothesis for a distribution and then
test that hypothesis.

### Possible approach

The issues of experimental design could be discussed as a
class. The interactivity purposely does not provide the time
between stars disappearing and reappearing. Students will need to
realise this and then suggest ways of gathering these data. There
will be questions of measuring the data and it is hoped that
students will realise that
collecting the data will involve a reaction delay and might relate
this to the original purpose of measuring the reaction time.
Students should be encouraged to design the experiment as
rigorously as they are able to, given the practical constraints of
having to run the interactivity to collect the data. (Note: they
will probably need their own stopwatch)

How can the data be analysed once collected? Students can
apply statistical concepts as appropriate to their level of study.
The data can be represented in ways appropriate to their level of
study. They might then begin to suggest possible distributions to
fit the data.

It is hoped that, given enough data, students will notice that
there are no very short times and no very long times. Would this be
compatible with normal or Poisson distributions?

### Key questions

How are we to collect the times for the stars to appear?

Is there a reaction delay in collecting this time?

How might we design the experiment to minimise the effects of
reaction time uncertainty?

What distributions or statistical measures do we know?

Once we have our data how might we rule out certain
distributions?

How much data would we need to be confident in a final
hypothesis?

### Possible extension

This task naturally offers differentiation by outcome. Students
might want to try to write up clearly the process for display;
collecting mathematical thoughts in this way is a useful exercise.

### Possible support

Suggest measuring data and plotting a histogram of times with
an interval of 0.5 seconds to begin to get a feel for the
data.

Alternatively, you can use the reaction timer to pose and test
your own hypotheses about reaction. You might like to see the
problem

Reaction
Timer to get some ideas.