2. 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.
3. 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
4. 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.
5. 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.
6. 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.
7. 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.
8. 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
9. 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.
10. 1.7 Critical Evaluation
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.
11. 1.7 Critical Evaluation
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.
12. 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.
13. 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?
14. 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.
15. 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?
Population: All dog owners in Whatcom CountySample: dog owners who came in to Petsmart on the day of the surveyParameter: number or proportion of dog owners in whatcom county who would use each locationStatistic: number or propotion of dog owners who come in to Petsmart on the day of the survey who would use each locationVariable: X = prefered location of a dog ownerData: the specific values of X
Population: All dog owners in Whatcom CountySample: dog owners who came in to Petsmart on the day of the surveyParameter: number or proportion of dog owners in whatcom county who would use each locationStatistic: number or propotion of dog owners who come in to Petsmart on the day of the survey who would use each locationVariable: X = prefered location of a dog ownerData: the specific values of X
Population: All dog owners in Whatcom CountySample: dog owners who came in to Petsmart on the day of the surveyParameter: number or proportion of dog owners in whatcom county who would use each locationStatistic: number or propotion of dog owners who come in to Petsmart on the day of the survey who would use each locationVariable: X = prefered location of a dog ownerData: the specific values of X
Population: All dog owners in Whatcom CountySample: dog owners who came in to Petsmart on the day of the surveyParameter: number or proportion of dog owners in whatcom county who would use each locationStatistic: number or propotion of dog owners who come in to Petsmart on the day of the survey who would use each locationVariable: X = prefered location of a dog ownerData: the specific values of X