Sampling Variability
Section 8.1
Let’s explore

Find a point estimate of the area of the
rectangles on the page.
 How
many should we sample?
 Use Math – PRB – RandInt(1,100, n)
Questions

Do all of your trials contain the true mean of 7.4?

What’s the shape of the graph?

If mean is 7.4 and standard deviation is 5.126 ,
what is the mean & standard deviation of the
sampling distribution?
Sampling Distribution

Represents the long run behavior of the
mean when sample after sample is
selected.

It is used to find out more about a
parameter of a population.
Parameter

Quantity computed from values in a
population
 Usually


p
not known
Statistic

Quantity computed from values in a
sample.
 Computed
x
s
p
directly from sample data
Identify the population, parameter,
sample and statistic.

The Gallup Poll asked a random sample of 515 U.S.
adults whether or not they believe in ghosts. Of the
respondents, 160 said “yes.”
Identify the population, parameter,
sample and statistic.

On Tuesday, the bottles of Arizona Iced Tea filled in a
plant were supposed to contain an average of 20 ounces
of iced tea. Quality control inspectors sampled 50
bottles at random from the day’s production. These
bottles contained an average of 19.6 ounces of iced tea.
Identify the population, parameter,
sample and statistic.

On a New York-to-Denver flight, 8% of the 125
passengers were selected for random security screening
before boarding. According to the Transportation
Security Administration, 10% of passengers at this
airport are chosen for random screening.
Sampling Variability
The observed value of a statistic will depend
on the sample selected.
In other words – it will vary from sample to
sample.
Sampling Distribution

Distribution of the values of a statistic

Notice what the relationship is between
the mean of the population & the sample.
Abby -24
Bill – 25
Cindy- 26
Dave – 27
Ed – 28
Find the sampling distribution if we
look at samples of size 2. (sample with
replacement – do all combinations!)
{2, 4, 6, 8} – Size 2 samples - mean
{2, 4, 6, 12} – Size 2 samples range
Unbiased Estimator

If the mean of the sampling distribution is
equal to the true value of the parameter
being estimated.
Sampling Heights
Write name and height in inches on paper.
 Each person will take a sample of 4.
 Find the sample mean – put on dotplot
 Find the sample range – put on dotplot

Variability of a Statistic

The spread of the sampling distribution
does not depend on the size of the
population, as long as the population is at
least 10 times larger than the sample size.
Homework
Page 428 (1-19)odd, (21-24)
 For the population {10, 12, 14, 16}, find the
following for a sample size of 2:

 A.
Sampling distribution of means
 B. Sampling distribution of range