AP Statistics
Notes
Name: ____________
Date: _____________
Lesson 9.1A: Simulating a Sampling Distribution –
The German Tank Simulation
Learning Targets:
A: Identify parameters and statistics in a sample or experiment.
B: Recognize the fact of sampling variability: a statistic will take different values when you repeat a sample.
C: Interpret a sampling distribution of a statistic as describing the values taken by a statistic in all possible
repetitions of a sample or experiment under the same conditions.
D: Describe the bias and variability of a statistic in terms of the mean and std.dev. of its sampling distribution.
E: Understand that the variability of a statistic is controlled by the size of the sample.
Vocabulary:
parameter
statistic
sampling distribution of a statistic
unbiased statistic
sampling variability
Introduction to Sampling Distributions
In the German Tank Simulation, you determined point estimates for the total number, N, of
tanks in the German army. In fact, for each random sample of size 5 (n = 5), you actually
calculated 5 or 6 point estimates using the formulas provided by each group. To keep this
simple, just focus on the formula (estimator) that your group developed.
Sample
Population
In general:
In general:
Sample Statistic –
Population Parameter -
German Tanks:
German Tanks:
Sample Statistic -
Population Size -
Means:
Means:
Sample Mean -
Population Mean –
Sample Standard Deviation –
Population Standard Deviation -
Proportions: (Binomial with a twist!)
Proportions: (Binomial with a twist!)
Sample Proportion –
Population Proportion -
Next, you used your formula to calculate the value of your sample statistic for 10 different
random samples drawn from the same population. Would you expect the value of your
sample statistic to be the same from sample to sample? Why or why not?
Sampling Variability –
Then as a class, we generated about ______ random samples of size n = 5.
Now you have a distribution of values of your sample statistic obtained from approximately
_____ random samples of size n = 5. This is a rough approximation of the sampling
distribution of your sample statistic.
Sampling distribution of a statistic –
Construct a histogram of the sampling distribution of your sample statistic.
Don’t forget to CUSS and BS !!
Center:
Spread:
Shape:
Is the mean of your approximated sampling distribution of your sample statistic close to the
actual number of German tanks in the population?
Unbiased Statistic –
While it is important for the mean of a sampling distribution of a sample statistic to equal the
corresponding population parameter, it is also important to consider the spread, or variability,
of the sampling distribution.
Low Variability
High Variability
Unbiased Statistic
Biased Statistic
Which combination of unbiased/biased statistic and low/high variability is most desirable?
Why?
Now, let’s talk notation: (Don’t let it get you !!)
Sample
Statistic
Sampling
Distribution of
Sample Statistic
Population
Parameter
Mean:
Standard
Deviation:
The ideal situation is to have:
an unbiased statistic _______________________________
and small sampling variability ________________________.
Classify the following histograms in terms of low/high bias and low/high
variability.
a. __________________________
__________________________
b. __________________________
__________________________
c. __________________________
__________________________
d. __________________________
__________________________