#### Transcript Sample

```Parameters VS. Statistics
and
Samples & Census
How do we compare
statistics and parameters?
M2 Unit 4: Day 3
Statistics VS Parameters
Statistics (for samples) :
x and S
Parameters (for populations) :
 and 
Today…



You will be given the population
parameters  and 
You will be given a data set for a sample
and you will find the statistics x and S
Then you will compare the statistics to
the parameters
Example1
For a large population, the mean  =
25.1 and the s.d  =5.3.
A random sample produced the following data values:
25, 21, 32, 14, 17, 22, 29.
Compare the mean and s.d of the random sample to
the population parameters.
Sample
x  22.86
S x  6.36
Population
  25.1
 x  5.3
The mean of the sample is
less than population mean
while the s.d. of the sample
is greater than the
population s.d.
Example 2
For a large population, the mean  =
4.8 and the s.d  =3.6.
One random sample produced the following data
values: 5, 1, 3, 4, 7, 6, 8, 2, 1, 3.
Compare the means and s.d’s of the random samples
to the population parameters.
Sample 1
x4
S x  2.45
Population
  4.8
 x  3.6
The mean and standard
deviation of the sample are
less than population mean
and the population s.d.
Example 3
For a large population, the mean  =
12.3 and the s.d  =4.24.
One random sample produced data values of
21, 13, 15, 12, 20, 22, 16, 18.
Another random sample produced data values of
14, 15, 12, 20, 29, 18.
Compare the means and s.d’s of the random samples
to the population parameters. The mean of the both
Sample 1
Sample 2
x  17.13
S x  3.72
x  18
S x  6.10
Population
  12.3
 x  4.24
samples are greater than
population mean. The s.d. of
the 1st sample is less than
that of the population s.d
while the s.d. of the 2nd
sample is greater than the
population s.d.
Example 4: Compare Statistics and Parameters
Population
  18.4
 x  15.6
Gillian
Ted
x  17.8
S x  12.35
x  21.1
S x  14.52
less than
greater than
less than
Example 5: Compare Statistics and Parameters
A teacher wants to know how often her students study at
night. Random samples are collected from John and
Sally, two students. Their results are given below. The
population mean is 1.24 and the population standard
deviation is about 2.32. Compare the means and
standard deviations of the random samples to the
populations parameters. John: .35, 1.23, .55, 2, 3.1
Sally: 1.1, .46, 2.3, .25, 2.2
John
Sally
x  1.45
S x  1.13
x  1.26
S x  0.96  x  2.32
Population The mean of the both samples are
  1.24 greater than population mean.
The standard deviations of both
samples are less than that of the
population standard deviation.
Comparing
A Population and A Sample

A population is a group of people or objects
• “ the whole”, everything or everyone which is
relevant

A sample is a subset of the population
• “the part”, just a piece of the population
Example: ECHS student survey
• sample = 1 student from each class
• population = all the students in the school
Example:
Each week, the Gallup Poll questions about
1500 adult US residents to determine
national opinion on a wide variety of issues.


What is the population?
Population = all US residents that week
Who is the sample?
Sample = 1500 US residents questioned
Random Sample

A sample in which each member of the
population has an equal chance of being
selected.
Examples:


Putting everyone’s name in a hat and pulling one out.
Having a computer randomly generate a list of items.
Representative samples

A)
B)
C)
A principal wants to know if teachers would
be willing to give \$1.00 each week to help
provide new text books for the students.
Which would give a representative sample?
Ask teachers who have first period planning
Ask the teachers that want new text books in
their classrooms
Representative random samples

The following list provides the average number of
cookies baked for a bake sale. A food inspector
wants to choose samples of cookies to inspect.
Choose a method of random selection that is
Joe
20
Sally
12
Jane
28
A) choose the first cookie baked by each person
B) choose at random, 2 cookies from each person
from Sally and 7 cookies from Jane
Representative random samples

The following list provides the average number of tshirts made by a t-shirt company. The manager
wants to choose samples of t-shirts to inspect.
Choose a method of random selection that is
Black
1500
representative of all t-shirts.
White
1250
Red
1000
A) choose 5 black t-shirts, 10 white and 50 red
B) choose at random, 30 Black shirts, 25 White shirts
and 20 Red shirts
C) choose at random, one of each shirt
Samples
Unbiased vs. Biased


Unbiased (FAIR) Sample:
A representation of the population you
Biased Sample:
A sample that over represents the
population or under represents part of
the population.
Examples:
1. A pharmacy wants to find out if its customers
would be interested in ordering their
prescription through their website.
Asking every third prescription customer if they
would be interested would be an ______
unbiased sample.
2. A movie theater wants to know which day of
the week its customers prefer to see movies.
A biased sample would be to ask the question to
all of its customers on Thursday.
Examples:
3. A school is trying to find out what is the
favorite sport among the students.
Asking every other football player, “What is your
biased sample.
favorite sport?” would be a
4. A store wants to know which style of jeans
customers prefer.
An unbiased sample would be to ask every
other customer what their favorite style of jeans
is.
Census

Every individual in the population is
contacted
• not really practical because they are very time
consuming and extremely costly.

Example:
• the US does a census every 10 years.
It tries
to contact everyone in the US and asks them
questions about race, ethnicity, # of people in
their house hold, etc.
The next census will occur in 2020.
Assignment:


Pg. 275 # 6 – 8, 11
Pg. 276 # 1, 2, 4 – 6
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