STATS 210
Team Task 2
Marks are awarded for attendance and participation.
Use these sessions to practice your creativity and ingenuity.
Do not leave until your team has spoken with a tutor!
Can you cheat with dice by baking them?
Several internet sites claim that you can bake dice to make them more
likely to come up with the numbers you want. Some sites claim that 10
minutes of baking will be enough to fix the dice to come up with your
numbers every time! The following instructions are from
www.ehow.co.uk/how_6403468_make-fixed-dice.html
and the pictures are from
www.buzzfeed.com/koolnewsblog/how-to-bake-a-cheating-dice-1dgl.
1. Place dice on a baking tray with the number you want face up.
2. Bake in a conventional oven at about 120◦ Celsius for 10 - 20
minutes.
3. The plastic in the dice melts slightly and sinks to the bottom,
making the dice heavier on that side and more likely to fall
with that face downwards.
NOTE: if you try this at home, be sensible, do not leave unattended,
and make sure the area is well-ventilated! Remember that melting
plastic gives off toxic fumes.
Does it work?
Your team is provided with two dice that have been baked according to this recipe:
• A Red or White die: these have been treated to come up with a 6;
• A Blue or Green die: these have been treated to come up with a 1.
Task 1:
With your team, conduct an investigation to assemble and analyse evidence about whether
baking the dice has changed your chances of throwing a 6.
You must:
• Use the Red or White die that has been treated to come up with a 6.
• Roll the die onto paper or a coursebook, to avoid too much noise.
• Decide how many rolls you will use. You will need to use the Binomial tables provided,
so pick your number of rolls accordingly.
In your write-up:
Write up your investigation, in particular your statistical analysis, using the style in the
coursebook.
• Give your Method.
• Give your Results.
• Give your Statistical Analysis.
• Give your Conclusions.
Task 2:
If you have enough time, have a go at the following problem. You have also been given a
Blue or Green die that has been treated to come up with a 1: the opposite of a 6. If the
method works, your Red/White die should be weighted in favour of 6, and your Blue/Green
die should be weighted against 6.
You want to test the following hypothesis:
H0 : the Red/White die and the Blue/Green die are equally likely to show a 6.
Normally, this investigation would be done using a two-sample test, like the two-sample
t-test. However, using a bit of ingenuity, it is possible to test it using a single Binomial test
like the ones we have already studied in lectures.
Devise a way of testing this hypothesis using one Binomial test. Conduct your investigation,
and write up your method, results, analysis, and conclusions as a team.
Hints:
• For a Binomial test, you need two outcomes: success or failure.
• You have two dice, and each of them can give a 6 or not a 6. How can you make this
situation into a two-outcome situation?
A really useful hint. . .
• If you had two runners and you wanted to test which was better, would you race them
together or separately? And how would you decide which was better?
Another hint. . .
• Could you only use part of the data, instead of all of it, to make two outcomes?
Get an answersheet from the tutor and discuss your answers
before you leave!