Transcript AP Statistics

AP STATISTICS
Section 5.1 Designing Samples
Objective: To be able to identify and use different sampling
techniques.
Observational Study: individuals are observed and
variables of interest are measured. No influence on the
responses.
Experiment: actively impose a treatment on a group in
order to observe a response.
Population: the entire group of individuals that we desire
information about.
Sample: a subset of the population that we actually
examine in order to gather information about the
population.
Census: attempts to contact every individual in the entire
population.
Sampling Method: the process used to choose the sample.
Sampling frame: the actual list of individuals from which the
sample is actually selected.
Types of Sampling Techniques:
1. Voluntary Response Sample: consists of individuals
who choose themselves to respond to a general appeal.
2. Convenience Sample: sampling which chooses
individuals that are easiest to reach.
Biased: systematically favors certain outcomes.
3. Simple Random Sample: (SRS) a sample of size n in
which each individual has the same chance of being
selected and each set of n individuals has the same
chance of being selected.
Steps:
1. Label subjects. Using the RNT:
• <10 use digits 0 – 9
• 11 – 100 use digits 00 – 99
• 101 – 1000 use digits 000 – 999 (and so on)
2. Select x digits at a time.
3. Skip repeats and specified digits.
4. Stopping rules
Ex. Select a sample of size 3 from students in this class
using line 110 of the RNT.
4. Probability Sample: a sample chosen by chance. We
must know what samples are possible and what chance
each sample has.
5. Stratified Random Sample:
a.
b.
c.
Divide the population into groups of similar individuals called
strata.
Choose an SRS from each strata.
Combine all the SRSs to form the one sample
Ex. Choose a stratified random sample of size 4 from a
population that has 20 individuals (15M / 5F). Use line 120
from the RNT to do so.
6. Cluster Sample:
a. Divide the population into heterogeneous groups (clusters).
b. Assign each cluster a number.
c. Choose an SRS of the clusters.
d. Combine all the members of the randomly selected clusters to
form the sample.
Ex of clusters:
7. Multistage Sample: restricts random selection by
choosing the samples in stages. Uses multiple
sampling techniques within the sampling process.
Ex.
8. Systematic Random Sample:
𝑁
𝑛
a.
Begin by finding k. 𝑘 =
b.
Think of the population in k groups.
Randomly select the first subject/unit by randomly selecting a
number from 1 to k.
This subject/unit is the first member of the sample. Continue to
add k to this first number to get the remaining members of the
sample.
c.
d.
Ex. Choose a Systematic Random Sample from a class of
24 students where n = 4.
Types of Bias:
1. Undercoverage: occurs when some subgroup of the
population is unintentionally left out of the sampling
process.
2. Nonresponse: occurs when an individual chosen for the
sample can’t be contacted or refuses to cooperate.
3. Response bias: when the behavior of the interviewer or
the respondent affects the results.
4. Wording of the Question: when the phrasing of the
questions leads to biased results.
*Larger samples give more accurate and less variable
results. However, if the data is poorly collected there is no
way to fix biased results.