7.6 M2

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Chapter
7.6 M2
Sample Data Populations EQ How can we collect
data from populations?
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The Sample Plan is the process followed to select
units from the population to be used in the sample
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Basic Concepts in Samples and Sampling

• Population the entire group under study as
  defined by research objectives. Sometimes called
  the universe.
• Researchers define populations in specific terms
  such as heads of households, individual person
  types, families, types of retail outlets, etc.
  Population geographic location and time of study
  are also considered.

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Basic Concepts in Samples and Samplingcont.

• Statistic a numerical description of a sample
  characteristic
• parameter a numerical description of a
  population characteristic. The mean of a
  population is an example of a population
  parameter.
• Population mean The true mean of the entire
  population

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Reasons for Taking a Sample

• Practical considerations such as cost and
  population size
• Inability of researcher to analyze large
  quantities of data potentially generated by a
  census
• Samples can produce sound results if proper rules
  are followed for the draw

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Probability Sampling Methods Simple Random
Sampling

• Simple random sampling the probability of being
  selected is known and equal for all members of
  the population
• Blind Draw Method (e.g. names placed in a hat
  and then drawn randomly)
• Random Numbers Method (all items in the sampling
  frame given numbers, numbers then drawn using
  table or computer program)
• Advantages
• Known and equal chance of selection
• Easy method when there is an electronic database

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Ex 1 Collect data by random sampling

• A country club has 345 social members and 876
  golf members. The president of the country club
  wants to form a random sample of 20 social
  members and a separate random sample of 50 golf
  members to answer some survey questions. Each
  social member has a membership number from 1-345
  and each golf member has a membership number from
  1001 to 1876. Use a graphing calculator to select
  the members who will participate in each random
  sample.

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The Solution Keystrokes math, prb, 5(randInt)

• Use the random integer feature of a graphing
  calculator to generate 20 random integers between
  1 and 345.
• Use the arrows to scroll over and see the rest of
  the random values.
• Document the values this list makes up your
  random sample of social members.
• Now use the random integer feature to generate 50
  random integers between 1001 and 1876.
• Use the arrows to scroll over and see the rest of
  the random values.
• Document the values this list makes up your
  random sample of golf members.

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Ex2 Compare statistics and parameters

• A schools math club wants to know how many hours
  students spend on math homework each week.
  Savannah and Miguel, two students in the math
  club, collect separate random samples. Their
  results are displayed on page 274 of the M2
  textbook.
• The population mean is 11.9 and the population
  standard deviation is about 6.7. Compare the
  means and the standard deviations of the random
  samples to the population parameters.

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Lets compare results

• Savannah
• X-bar 9.8
• Std. deviation 3.6

• Miquel
• X-bar 12.7
• Std. deviation about 4.2

• The mean of Savannahs sample is less than the
  population mean.
• The mean of Miguels sample is greater than the
  population mean.
• The standard deviations of both samples are less
  than the population standard deviation.
• This indicates that the samples are less varied
  than the entire population.

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Homework
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