Chapter 3 Section 3

1
Chapter 3 Section 3

• Sampling Design

2
Population and Sample

• The entire group of individuals that we want
  information about is called the population.
• A sample is a part of the population that we
  actually examine in order to gather information.
• The design of a sample refers to the method used
  to choose the sample from the population.
• Example 3.14 3.15

3
Voluntary Response Sample

• A voluntary response sample consists of people
  who choose themselves by responding to a general
  appeal. Voluntary response samples are biased
  because people with strong opinions, especially
  negative opinions, are most likely to respond.

4
Simple random samples

• A simple random sample (SRS) of size n consists
  of n individuals from the population chosen in
  such a way that every set of n individuals has an
  equal chance to be the sample actually selected.
• Example 3.16

5
Stratified samples

• A probability sample gives each member of the
  population a known chance (greater than zero) to
  be selected.
• An SRS is a probability sample
• To select a stratified random sample, first
  divide the population into groups of similar
  individuals, called strata. Then choose a
  separate SRS in each stratum and combine these
  SRSs to from the full sample.
• Example 3.17

6
Multistage samples

• Multistage samples select successively smaller
  groups within the population in stages, resulting
  in a sample consisting of clusters of
  individuals. Each stage may employ an SRS, a
  stratified sample, or another type of sample.

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Undercoverage and Nonresponse

• Undercoverage occurs when some groups in the
  population are left out of the process of
  choosing the sample.
• Nonresponse occurs when an individual chosen for
  the sample cant be contacted or does not
  cooperate.
• Example 3.18

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• Response bias is due to the behavior of the
  interviewer or the respondent, or from misleading
  results due to poorly worded questionsIm
  looking at you Mike.
• Example 3.19Hey Mikelook familiar

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Daily Work

• Pg 262 -267
• 38 42

10
Chapter 3 Section 4

• Toward Statistical Inference

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Statistical Inference

• Statistical inference is a process in which we
  infer conclusions about the wider population from
  data on selected individuals.

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Parameters and Statistics

• A parameter is a number that describes the
  population. A parameter is a fixed number, but in
  practice we do not know its value.
• A statistic is a number that describes a sample.
  The value of a statistic is known when we have
  taken a sample, but it can change from sample to
  sample. We often use a statistic to estimate an
  unknown parameter.
• Example 3.20

13
Sampling variability

• Sampling variability is the value of a statistic
  varies in repeated random sampling.
• Example 3.21 simulation
• Individual work collect 3 sets of 10 for example
  3.21 and lets put it into an histogram.

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Sampling distributions

• The sampling distribution of a statistic is the
  distribution of values taken by the statistic in
  all possible samples of the same size from the
  same population.
• Figure 3.6 and 3.7
• Normal shape, mean and median is very close to
  the approximate value, the spread has a small std
  dev.
• Figure 3.8

15
Unbiased Estimator

• A statistic used to estimate a parameter is
  unbiased if the mean of its sampling distribution
  is equal to the true value of the parameter being
  estimated.

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The variability of a statistic

• Example 3.22
• The variability of a statistic is described by
  the spread of its sampling distribution. This
  spread is determined by the sampling design and
  the sample size n. Larger samples have smaller
  spreads.
• As long as the population is much larger than the
  sample, the spread of the sampling distribution
  for a sample of fixed size n is approximately the
  same for any population size.

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Bias and variablility

• Figure 3.9
• High bias
• Low bias
• High variability
• Low variability
• Example 3.23

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Daily Work

• Pg 277-281
• 58, 60, 62