SAMPLING
INVESTIGATION 5
Objective : Use samples of various sizes to obtain a sample proportion close to the Population
Proportion
Population Proportion – the proportion of the population that has the property
under investigation.
Procedure: This activity can be modelled using cube a links
34 black blocks 66 other
Read steps B, C, D on page 184 and complete the table below
Sample Size
Number of
Black Selected
% of sample
black
Estmate of black
in total
population using
sample
proportion
10
20
Complete Investigation Questions 22 and 23 on page 185
Complete Check Your Understanding Questions 24 and 25
40
80
UNIT 5:3
INVESTIGATION 6
***
Objective : Examine a Sampling Distribution for an experiment in which the outcomes are
equally likely.
Sampling Distribution : the distribution of results of an experiment or survey.
Often the distribution reflects the mean or the proportion of the sample.
Procedure : Make a list of the possible number of heads that occur when you toss four coins at
once.
( classroom discussion)
Now toss four coins at once and count the number of heads that occur.
Record the results in a table like the one below.
( You are actually tossing four coins at once for a total of 20 trials)
Alternate Procedure: Place four unit Algae tiles in a plate cover with a textbook and shake the
container counting the number of red ( heads ) 20 times.
Calculator TI – 83 randBin( 4, .5, 20 ) store L1
Data Table for B and C
Number of Heads
Tally
Frequency
Proportion of 20
trials
4
3
2
1
0
Repeat the process of 20 trials 20 times or pool your results with 20 other students
Equlivent to 20 * 20 trials
Number of Heads
Tally
Frequency
Proportion of 400
trials
4
3
2
1
0
Make a frequency bar graph of your results. Part D of Instructions
Part E Calculate the experimental probability of each possible number of heads. Display the
results creating a bar graph, with the probability on the vertical axis instead of frequency.
Note we are looking for the Experimental Probability.
THEORETICAL PROBABILITY
Number of heads
Number of
Favourable outcomes
3
2
1
0
Note catalogue command binompdf ( 3,0.5,{0,1,2,3}) store L1
Complete Focus questions 5 , 6
Complete Check Your Understanding 7,8
Theoretical probability
Investigation 7
Objective : Observe how “ large number of samples” produce a better match between the
“experimental” and “ theoretical “ probability distributions.
Procedure : Use your data from investigation 6 ( tossing 4 coins 20 times and observing the
number of heads produced) However this time pool you results with 9 other students and
complete the table below.
Alternate TI – 83 ( 4, .5, 20 ) Store L1
Each Student does this or (4,0.5,200)storeL2
Table:
Student
Number
Of
Heads
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Total Proportion Experimental
of 200
Probability
trials
Use the table to make a bar graph that shows the experimental probability of each number of
heads based on a large number of repetitions.
Which activity, Investigation 6 or investigation 7 , produced a better match with the theoretical
probability distribution? Why?
You can use your calculator to calculate the Theoretical probability
INVESTIGATION 8
Purpose : to model a binomial experiment in which
The number of trials is very large
The two outcomes of each trial are equally likely
Procedure: Use a calculator to model 50 repetitions of an experiment in which you toss a fair
coin 14 times ( or toss 14 fair coins) store the number of heads in list L1 of your calculator.
Randbin ( 14,.5,50) storeL1
After obtaining your list use the calculator to produce a probability bar graph and copy it into
your notes.
Window settings X min X max
0 , 15 respectively
Y min Y max
0 , 20 respectively
Use a calculator to model 500 repetitions of an experiment in which you toss a fair coin 14 times
( or toss 14 fair coins) store the number of heads in list L1 of your calculator.
Randbin ( 14,.5,500) storeL1
After obtaining your list use the calculator to produce a probability bar graph and copy it into
your notes.
Window settings X min X max
0 , 15 respectively
Y min Y max
0 , 200 respectively
Theoretical Probability
Step E
Please read all instructions carefully.
To allow the calculator to calculate the theoretical probability of tossing 14 coins and the
number of possible heads obtained perform the following operation on the calculator
In order to plot the theoretical probability enter into L1 the outcome values
1,2,3,4,5,6,7,8,9,10,11,12,13,14