1. Section 5.1 Designing Samples
AP Statistics
Section 5.1 Designing Samples

2. 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.

3. 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.

4. Types of Sampling Techniques:
Voluntary Response Sample: consists of individuals who choose themselves to respond to a general appeal.
Convenience Sample: sampling which chooses individuals that are easiest to reach.
Biased: systematically favors certain outcomes.

5. 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)
Select x digits at a time.
Skip repeats and specified digits.
Stopping rules

6. Stratified Random Sample:
Ex. Select a sample of size 3 from students in this class using line 110 of the RNT.
Probability Sample: a sample chosen by chance. We must know what samples are possible and what chance each sample has.
Stratified Random Sample:
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

7. 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.
Cluster Sample:
Divide the population into heterogeneous groups (clusters).
Assign each cluster a number.
Choose an SRS of the clusters.
Combine all the members of the randomly selected clusters to form the sample.
Ex of clusters:

8. Systematic Random Sample:
Multistage Sample: restricts random selection by choosing the samples in stages. Uses multiple sampling techniques within the sampling process.
Ex.
Systematic Random Sample:
Begin by finding k. 𝑘= 𝑁 𝑛
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.

9. Ex. Choose a Systematic Random Sample from a class of 24 students where n = 4.
Types of Bias:
Undercoverage: occurs when some subgroup of the population is unintentionally left out of the sampling process.
Nonresponse: occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate.

10. Wording of the Question: when the phrasing of the questions leads to biased results.
Voluntary Response Bias
Convenience Bias
Response bias: when the behavior of the interviewer or the respondent affects the 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.