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Section 1.2 Random Samples 1.2 / 1 Sampling techniques • Simple Random Sampling • Stratified Sampling • Systematic Sampling • Cluster Sampling • Convenience Sampling 1.2 / 2 • 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. Not random sampling: Ask for volunteers to respond to a survey. Choose the next five customers entering a store. 1.2 / 3 Random sampling: • Draw names “from a hat.” • Use a random number table to select a sample. • Use a random number generator. How to draw a random sample: 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. 1.2 / 4 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 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 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 “kth” item. Cluster Sampling • Population is divided into sections. • Some sections are randomly selected. 1.2 / 7 • Every item in selected sections is included in sample. 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 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 Which sampling technique is described? College students are waiting in line for registration. Students are asked to volunteer to respond to a survey. Convenience sampling 1.2 / 10 Which sampling technique is described? In a large high school, students from every homeroom are randomly selected to participate in a survey Stratified sampling 1.2 / 11 Which sampling technique is described? An accountant uses a random number generator to select ten accounts for audit. Simple random sampling 1.2 / 12 Which sampling technique is described? 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 1.2 / 13