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Very Old Man

Is the age of this very old man statistically believable?

Reaction Timer Timer

Stage: 5 Challenge Level: Challenge Level:1

Why do this problem ?

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.