1. 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: 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.

5. 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

6. 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. Divide the population into groups of similar individuals called strata. b. Choose an SRS from each strata. c. 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. 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:

9. 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.

10. 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.