Transcript How can we collect data from populations?

Chapter 7.6 M2
Sample Data & Populations
EQ: How can we collect
data from populations?
The Sample Plan is the process followed to select
units from the population to be used in the sample
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.
Basic Concepts in Samples and Sampling
• Sample: a subset of the population that should
represent the entire group
• Sample unit: the basic level of
investigation…consumers, store managers, shelffacings, teens, etc. The research objective
should define the sample unit
• Census: an accounting of the complete
population
Basic Concepts in Samples and
Sampling…cont.
• 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
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
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
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.
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.
Ex2: Compare statistics and parameters
• A school’s 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.
Let’s compare results
• Savannah
• X-bar: 9.8
• Std. deviation: 3.6
• Miquel
• X-bar: 12.7
• Std. deviation: about 4.2
•The mean of Savannah’s sample is less than the population mean.
•The mean of Miguel’s 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.
Homework
page 276 #1-7 all, 9