Predict your score
•
•
•
•
•
You are about to take a multiple choice probability test. It is from a
Canadian University but there is nothing in it that is beyond S1. Test
from http://www.stat.sfu.ca/~cschwarz/MultipleChoice/
There are 9 questions. Decide how many you think you will get right
and write your prediction down somewhere.
Do the test.
Mark it.
Add yourself to the tallies in the contingency tables.
Predicted
Actual
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
Score less than
prediction
Score equal to
prediction
Score above
prediction
Male
Female
What will students learn from this?
• Using contingency tables to look for association both qualitatively and
using Chi squared tests.
• Do students get more realistic about their scores as the course
progresses?
Guess the Age
(photos from www.ageguess.com and
http://www.channel4.com/life/microsites/0-9/10yy/guessmyage/ )
What will students learn from this?
Collecting the following data for each student gives a range of possibilities at a variety of
levels:
• error on each photo for each student (include whether it is positive or negative)
• mean error for each student
This should give examples of different distributions; skewed and symmetrical. It illustrates
that the picture of the distribution only emerges when you have enough data.
You could do boys and girls separately to look at questions such as “Are girls better at
guessing ages than boys?” or “Is it easier to guess the age of a male than of a female?” This
could lead to using measures of central tendency and spread to answer these questions.
Hypothesis testing is also a possibility for the null hypothesis “The mean error for girls
guessing is the same as for boys guessing”.
Or a paired test for a null hypothesis like: “The mean error on photo A is the same as on
photo C”.
What test(s) would be appropriate?
What’s in the bag?
•
•
•
•
•
The bag contains 20 multilink cubes. They are not all the same colour.
Take one out. Look at it and add its colour to the tally chart. Put it
back.
You can repeat this as often as you want.
When you are ready to guess the contents of the bag, write down what
you think is in it and you will be told if you are right.
We don’t believe in gambling, but, if we did, and if there was a prize for
the first person to guess the contents correctly:
o How much would you be willing to pay to have a guess?
o How much do you think you should win if you are the first to
guess correctly?
o When would you start paying to guess to make sure you are the
first one to get it right?
Colour Tally
What will students learn from this?
• This allows the exploration of ideas connected with sampling and
probability.
• It could be an introduction to ideas of expected win.
How many words do you know?
•
•
•
•
•
You may write on this sheet
The Oxford Pocket School Dictionary has 45 000 words and phrases in
it.
The words are on 800 pages with 2 columns a page and between 3
and 30 words a column.
You are going to sample 50 words at random. Which of these methods
will result in each word having an equal chance of being chosen:
o Choose a random number from 1 to 800 to choose a page.
Choose a random number from 1 to 40 and count to that word
on the chosen page. If there are less than 40 words on the
chosen page, go onto the next page (just keep counting).
o Choose a random number from 1 to 800 to choose a page.
Choose a random number from 1 to 40 and count to that word
on the chosen page. If there are less than 40 words on the
chosen page, start again at the top of the page (just keep
counting).
o Choose a random number from 1 to 800 to choose a page.
Toss a coin and use the left hand column for heads and the right
hand column for tails. Choose a random number from 1 to 20
and count to that word in the chosen column. If this random
number is too big, start again by choosing a new page.
o Flick through with your eyes closed, open the dictionary
anywhere and pick a word by putting your finger on the page
with your eyes closed.
Choose 50 words at random and, for each word, decide if you know it.
Use tally marks in this table to keep track of how many words you have
chosen and how many of them you know.
No. of
words
chosen
No.of
words
known
•
Use your sample and the fact that the dictionary contains 45 000 words to
estimate how many words you know.
What will students learn from this?
• Techniques for ensuring lack of bias in sampling.
• Thinking about what is meant by a random sample.
• Using a sample to make an estimate.
• More advanced students might construct a confidence interval for the
proportion of words they know.
Mazes
•
Have a go at Castle Bromwich maze and time yourself
•
Have a go at Hampton Court maze and time yourself
•
Put both times on the back to back stem and leaf diagram.
Mazes from http://www.cbhgt.org.uk/maze00.html
What will students learn from this?
• The obvious question is: how do times compare on the two mazes?
• A back to back stem-and-leaf diagram is one way to display the data
visually.
• What would be a suitable hypothesis test to use?