1. Section 1.2 Random Samples 1.2 / 1

2. Sampling techniques Simple Random Sampling Stratified Sampling Systematic Sampling Cluster Sampling Convenience Sampling 1.2 / 2

3. Simple Random Sample of n measurements from a population is a subset of the population selected in a manner such that Every sample of size n from the population has an equal chance of being selected. Every item in the population has an equal chance of being included. 1.2 / 3 Not random sampling: Ask for volunteers to respond to a survey. Choose the next five customers entering a store.

4. Random sampling: Draw names “from a hat.” Use a random number table to select a sample. Use a random number generator. 1.2 / 4 Number all members of the population Sequentially Use a table, calculator or computer to select random numbers from the numbers assigned to population members. Create the sample using population members with numbers corresponding to selected numbers. How to draw a random sample:

5. Simulation Provide mathematical imitations of “real” phenomena. May use a random number table to simulate a process. (Good in nuclear reactors, cloud formation, cardiology etc.) 1.2 / 5

6. Example of Simulation Use the random-number table to simulate the outcomes of tossing a balanced (that is, fair) quarter 10 times. (a) Possible outcomes: 2, heads or tails (b) Assign an even digit or heads and odd digit for tails. Then starting at block 3 of row 2 of table 1 in the appendix, list the 10 single digits 7 1 5 4 9 4 4 8 4 3 (c) The outcomes associated with the 10 digits T T T H T H H H H T (d) If you start with different block and row will you get the same sequence of outcomes? It is possible, but not very likely 1.2 / 6

7. Sampling Techniques Sampling with Replacement When a number is selected for a sample, it is not removed from the population. Stratified Sampling Population is divided into groups. Random samples are drawn from each group. Systematic Sampling Population is arranged in sequential order. Select a random starting point. Select every “k th ” item. Cluster Sampling Population is divided into sections. Some sections are randomly selected. Every item in selected sections is included in sample. 1.2 / 7

8. Sampling Techniques Convenience Sampling Use whatever data is readily available. Risk severe bias. Summary of Sampling techniques Random Sampling Stratified Sampling Systematic Sampling Cluster Sampling Convenience Sampling 1.2 / 8

9. Which sampling technique is described? College students are waiting in line for registration. Every eighth person in line is surveyed. Systematic sampling 1.2 / 9

10. Convenience sampling Which sampling technique is described? College students are waiting in line for registration. Students are asked to volunteer to respond to a survey. 1.2 / 10

11. Stratified sampling Which sampling technique is described? In a large high school, students from every homeroom are randomly selected to participate in a survey 1.2 / 11

12. Simple random sampling Which sampling technique is described? An accountant uses a random number generator to select ten accounts for audit. 1.2 / 12

13. To determine students’ opinions of a new registration method, a college randomly selects five majors. All students in the selected majors are surveyed. Cluster sampling Which sampling technique is described? 1.2 / 13