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Chapter 1

S A M P L I N G A N D D A TA
1.6 - 1.9

1.6 Sampling

 Random sampling is the process of using chance to select
individuals from a population to be included in the sample.

 If a sample is selected in a way that assures that any sample
of the same size would be equally likely to be chosen then
the sample is a simple random sample.

Pride and Prejudice
EXAMPLE The Sun Also Rises
Use a random number
generator to choose a The Jungle
simple random sample As I Lay Dying
of size three from the
list of classic works of A Tale of Two Cities
literature.
Huckleberry Finn
Death of a Salesman
Scarlet Letter
Crime and Punishment

1.6 Sampling

 A systematic sample is chosen by selecting every nth
individual in the population.
 A stratified sample is chosen by dividing the population into
nonoverlapping groups called strata and then selecting a
simple random sample from each stratum.
 A cluster sample is chosen by dividing the population into
strata and then selecting some of the strata.
 A convenience sample is a sample in which the individuals
are easily obtained and not based on randomness.

1. To estimate the percentage of defects in
EXAMPLE a recent manufacturing batch, a quality-
control manager at Intel selects every 8th
Identify the type of chip that comes off the assembly line
sampling used. until she obtains a sample of 140 chips.

2. To determine customer opinion of its
boarding policy, Southwest Airlines
randomly selects 60 flights during a
certain week and surveys all passengers
on the flight.

3. To determine DSL connection speed,
EXAMPLE Shawn divides up the day into four parts:
morning, midday, evening, and late night.
Identify the type of He then measures his Internet
sampling used. connections speed at 5 randomly selected
times during each part of the day.
4. 24 Hour Fitness wants to administer a
satisfaction survey to its current members.
Using its membership roster, the club
randomly selects 40 members and asks
them about their level of satisfaction with
the club.

5. A radio station asks its listeners to call in
EXAMPLE their opinion regarding the use of U.S.
forces in peacekeeping missions.
Identify the type of
sampling used.

 To find the average GPA of all students in
EXAMPLE a university, use all honor students at the
university as the sample.
Determine if each of
the following samples  To find out the most popular cereal among
are representative. young people under the age of 10, stand
outside a large supermarket for three hours
and speak to every 20th child

1.7 Critical Evaluation

There can be many problems with a statistical study.
 Problems with Samples: remember that we always want a
representative sample. Be sure your sampling method does
not lead to bias.
 Self-Selected Samples: Responses only by people who
choose to respond are often unreliable
 Sample Size Issues: Samples that are too small may be
unreliable.
 Undue Influence: Collecting data or asking questions in a
way that influences the response.


 Causality: A relationship between two variables does not
mean that one causes the other to occur.
 Self-Funded or Self Interest Studies: A study performed by
a person or organization in order to support their claim may
not be impartial.
 Misleading use of data: Improperly displayed graphs,
incomplete data, and lack of context can cause people to
come to incorrect conclusions.
 Confounding: occurs when the effects of multiple factors
on a response cannot be separated.


Key elements to statistical thinking:

 Anecdotal claims can be refuted with statistical analysis.

 Poorly collected data are not useful.

 Watch out for confounding variables.

 Results in statistics are not certain.

1.7 Key Terms

 The frequency is the number of times a given datam occurs
in a data set.

 The relative frequency is the fraction of times a given datum
occurs.

 The cumulative relative frequency is the accumulation of the
previous relative frequencies.

1. Construct a frequency table.
EXAMPLE
2. What percentage of students have 0
How many siblings
siblings?
do you have? 3. What percentage of students have 1 to 3
siblings?
4. What percentage of students have fewer
than 3 siblings? At least 3 siblings?

Data Frequency Relative Cumulative
EXAMPLE Frequency Relative
Frequency
Nineteen people 3 3 3/19 0.1579
were asked how 4 1 1/19 0.2105
many miles, to the
5 3 3/19 0.1579
nearest mile, they
commute to work 7 2 2/19 0.2632
each day. The data 10 3 4/19 0.4737
are:
12 2 2/19 0.7895
2, 5, 7, 3, 2, 10, 18, 13 1 1/19 0.8421
15, 20, 7, 10, 18, 5,
15 1 1/19 0.8948
12, 13, 12, 4, 5, 10
18 1 1/19 0.9474
The following table
20 1 1/19 1.000
was produced.

1. Is the table correct? If not, what is
EXAMPLE wrong with it?
2. True or false? Three percent of the
people surveyed commute 3 miles.
If the statement is false, what should
it be?
3. What fraction of the people
surveyed commute 5 to 7 miles?
4. What fraction of the people
surveyed commute at least 12 miles?
Less than 12 miles? Between 5 and
13 miles?

1.14 Lab 2
GROUP WORK

Split into groups of 3 to 4.

HOMEWORK

1.12 #s 3, 15, 16, 19-28

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Chapter 1 sections 6 through 9

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Chapter 1 sections 6 through 9

Editor's Notes