Finding Sales Tax by jennyyingdi

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									Sampling Methods

    Lesson 3-6
   Pg. # 103-105
          CA Content Standards
Statistics, Data Analysis, and Probability 2.2***:
I can identify different ways of selecting a sample (i.e.
   convenience sampling, responses to a survey,
   random sampling) and which method makes a
   sample more representative for a population.

Statistics, Data Analysis, and Probability 2.4***:
I can identify data that represent sampling errors and
   explain why the sample might be biased.
       Vocabulary: BIASED
 Survey results in which samples are
  chosen or used unfairly.
           Vocabulary:
        REPRESENTATIVE
 Containing typical examples of all types
  in a group.
       Vocabulary:
  CONVENIENCE SAMPLING
 Sample is formed by choosing individuals
  or objects that are convenient, or easy, to
  include in the study.

 Usually results in a biased sample.
          Vocabulary:
       RANDOM SAMPLING
 Sampling in which each individual or item
  has an equal chance of being chosen.

 Usually results in a representative, or fair,
  sample.
         Vocabulary:
    SYSTEMATIC SAMPLING
 Sampling that involves a system, method,
  or plan.

 Usually results in a representative, or fair,
  sample.
       Vocabulary:
 RESPONSES TO A SURVEY
 Answers to a questionnaire or other
  device designed to get information from a
  population.

 Usually results in a biased sample
  because only people who really care or
  have the time will respond to the survey.
              Objective


Understand how the method of
 sampling determines how
 representative the sample is of the
 population.
Math Link: You can use what you
 know about sampling to find how
 sampling methods can affect the
 statistical results.
   Example 1.

Look at the table on page 103. It shows the
 number of school districts in each state.
The five most populated states are
 California (CA), Texas (TX), Michigan (MI),
 Illinois (IL), and New York (NY). Find the
 median number of school districts per state
 using these five states as a sample.
       MI    NY       IL    CA      TX
      674    705     929    994    1042

The median is the middle number in the
 sample. According to this sample, there are
 approximately 929 school districts in each
 state.
A biased sample does not reflect the
 population fairly. This sample is biased
 because states with large populations are
 likely to have more than an average number
 of school districts.
 Example 2.

The name of each state was written on a
 piece of paper and placed in a bag. Then
 five pieces of paper were selected without
 looking.

The states selected were Maine (ME),
 Colorado (CO), Wisconsin (WI), Kansas
 (KS), and Rhode Island (RI).
       RI    CO      ME     KS      WI
       36    176     284    304     426

The median is the middle number in the
 sample. According to this sample, there are
 approximately 284 school districts in each
 state.
This example uses random sampling. In
 random sampling, each school district has
 an equal chance of being chosen. Since a
 random sample is usually a good match for
 the population, it is a representative
 sample.
     Example 3.

 The principal of an elementary school sent
   a survey letter to each student’s parents
  asking if voters in the school district would
     support a tax increase to build a new
                 middle school.

 Is this sample likely to be representative or
                      biased?
 The sample is biased. Parents of elementary
 students who would be attending the new school
  are more likely to support a new middle school
          than would voters in general.

 It was convenient for the principal to survey
 parents of students. In convenience sampling,
 any easy method is used to choose the sample.
              This is usually biased.

 Asking for responses to a survey is another
 form of sampling that is often biased. People with
 strong opinions are more likely to take the time to
    respond to a survey than people in general.
 Example 4.
Cassie wants to determine which brand
 of athletic shoes is most popular with
 U.S. middle school students. She
 decides to stand near the entrance of
 her school and keep a count of what
 brands of shoes students are wearing
 as they enter the school.
What sampling method is Cassie using?

Convenience Sampling

Is it likely to be representative or
 biased? Why?

It is likely to be biased since she is
   studying only students at her school.
     The Moral of the Story:
Random sampling is important for
 obtaining measures that accurately
 describe the population being studied.
 Convenience sampling and responses
 to surveys involve a bias.

								
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