Finite Population Sampling Flashcards

1
Q

Give two reasons why people choose to sample.

A
  1. Cheaper and faster than full census (could be impossible)
  2. May be more accurate (when census’s get too large quality control is harder)
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2
Q

What does N stand for?

A

Number of inidividuals in the population

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3
Q

What does xi stand for?

A

The value of x for individul i

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4
Q

What does θ stand for?

A

Population parameter, function of the population values.

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5
Q

Name four population parameters.

A
  1. Population average
  2. Population total
  3. Population variance
  4. Population standard deviation
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6
Q

What is the equation for population average?

A
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7
Q

What is the equation for population total?

A
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8
Q

What is the equation for population variance?

A
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9
Q

What is the difference between N and n?

A
  • N - Population size
  • n - Sample size
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10
Q

What is the number of possible samples, when using a simple random sample without replacement?

A
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11
Q

Define a statistic.

A

A statistic is any function of the sample observations.

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12
Q

Define a sampling distribution.

A

The sampling distribution of a statistic is:

  1. the set of possible values that the statistic can take
  2. the probability that the statistic takes each values
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13
Q

Are samples with smaller or larger variacnes more reliable?

A

Smaller

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14
Q

What is the difference between Ȳn and 𝜇?

A
  • Ȳn is the sample average
  • 𝜇 is the population average
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15
Q

Prove 𝔼(Ȳn) = 𝜇.

A
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16
Q

What does 𝔼(Ȳn) = 𝜇 show?

A

The sample mean is an unbiased estimator for the population mean.

17
Q

Define bias and therfore unbiased.

A

If statistic S estimates population parameter θ, then the bias of S is

b(S, θ) = 𝔼(S) - θ

If the bias is zero, then S is called unbiased.

18
Q

What does σȲn stand for?

A

Standard error of estimator Ȳn.

19
Q

Prove

20
Q

When N >> n what can you say about this inequality?

21
Q

For large N what does var(Ȳn) approximately equal?

22
Q

What does f stand for in this equation?

A

f is the sampling fraciton, n/N

23
Q

What is the equation for sample variance?

24
Q

What does sȲ stand for?

A

Estimated standard error of Ȳ

25
Complete this therom. 1. s2 is almost unbiased for σ2,, as ... 2. sȲ2 is an unbiased estimator for σȲ2, where ...
26
What are the possible values of xi when talking about binary outcomes?
0 or 1
27
Bianry outcomes - If the proportion of indviduals in the population with x = 1 is p what is 𝜇 and σ2?
* 𝜇 = p * σ2 = p(1-p)
28
If p^ is the proportion of individuals in sample with x=1 then what does Ȳ equal?
29
If p^ is the proportion of individuals in sample with x=1 then what does s2 equal?
30
If p^ is the proportion of individuals in sample with x=1 then what does σp^2 equal?
31
What is σp^2 smaller than?
32
What is the equation for the unbiased estimator for σp^2?
33