School Improvement in Maryland
Designing Samples/Simple Random Samples
 
Data Analysis and Probability .
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Objectives
 
  • The student will consider the advantages and disadvantages of various sampling techniques.
  • The student will define a Simple Random Sample and identify possible sources of bias in other types of samples
     
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Core Learning Goals
 
  • 3.1.1: The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results.
     
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Drill
 
  • Systematic error caused by bad sampling methods may lead to a biased study favoring certain outcomes.

    Identify possible sources of bias in each survey.

    1. Customers at a supermarket are sampled to determine their opinion about a controversial political issue.
      (Supermarket shoppers may share characteristics that differ from those of the general public. To include only these people in a sample you may not get the full range of public opinion.)
    2. Television viewers are invited to call an 800 number to report their opposition to a bill to increase state gasoline taxes.
      (This is an example of a voluntary response sample. To include in a sample only those that volunteer, one may tend to get only the opinions of those who feel very strongly about certain issues.)
    3. A large company selects names from a telephone book to sample for a survey on household spending habits.
      (Those with unlisted phone numbers or without phones will not be included in the sample. These people may have significantly different spending habits than those contacted.)
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materials
 
  • Activities: "Designing Samples," "Simple Random Samples," and "Examining Sample Designs"
  • Answer Keys

    • .  Print Version: (Acrobat 21k)
    The print version contains all student worksheets and answer keys needed to complete the lesson.
     

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Calculator Skills
 
  • NONE
     
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activities
 
  1. Drill. This activity introduces students to the concept of bias. Students need to recognize when bias is present in sampling design. Results from biased samples should not be used to estimate population percentages.
  2. Exploration. As mentioned earlier, not all samples will yield good estimates for a population percentage. These activities require students to analyze sampling methods and to consider sources of bias that may corrupt sample results. Under-representation of certain groups in a population or poorly worded questions can significantly alter sample results.
  3. Class Discussion. At this point students should see that the size of the sample must be relatively large and that the sample should be unbiased and representative of the population. Simple Random Sample techniques ensure that each member of the population has an equal chance of being selected for the sample.
  4. Additional problems. "Examining Sample Designs
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Assessment
 
  • Summary Questions:
    1. What is a simple random sample?
      (A simple random sample ensures that each member of the population is equally likely to be chosen and the members of the sample are chosen independently of each other.)
    2. Identify characteristics of good sample designs.
      (Sample should be large with respect to the population. They should be representative of the population, and they should be selected in a random fashion.)
       
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Homework
 
  • "Examining Sample Designs"
     
Objective Objective Core Learning Goals Core Learning Goals Drill Drill Materials Materials Calculator Skills Calculator Skills Activities Activities Assessment Assessment Homework Homework