1 chapter 2: sampling and surveys. 2 random sampling exercise choose a sample of n=5 from our class,...
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Chapter 2: Sampling and Surveys
2
Random Sampling Exercise
• Choose a sample of n=5 from our class, noting the proportion of females in your sample.
– RandInt
– Do this 3 times
• We’ll create a dotplot to display the proportion of females selected in each sample.
• How do our sample proportions relate to the actual proportion?
3
Simple Random Sample (SRS)
• Definition, p. 69
• Did we choose an SRS?
4
Biased Sampling Methods (p. 66)
• Voluntary response methods
• Convenience sampling
• Exercises, pp. 67-68: 2.1, 2.4
5
Back to SRS
• Some ways to choose and SRS:
– Drawing names from hats
– Using table of random digits
– Computer or calculator random numbers generator
• Steps for choosing SRS:
– p. 72
• Exercises: 2.7, p. 74 and 2.10, p. 75
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Calculator Corner, p. 73
• “Random” digits
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HW
• Reading: Section 2.1, pp. 63-80
• Exercises, pp. 80-82:
– 2.17, 2.19, 2.22, 2.23, 2.24
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Do you lotto?
• Read paragraph in blue, pp. 82-83.
• From sample to population, p. 85
– We take a sample from a population, and use the statistic to estimate the parameter of interest.
• Population … parameter
• Sample … statistic
• Notations
– Means and proportions
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Practice Exercises
• p. 86
– 2.25, 2.26
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Activity 2.2, p. 83
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Sampling Variability
• Our statistics were not the same every time. That is variability.
• How much variability will there be upon repeated samplings?
– Depends on the sample size.
– See Figures 2.3 (p. 87) and 2.4 (p. 88)
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Two types of error in estimation
• Bias
– Use random sampling to reduce bias.
• Sampling variability
– Use a larger sample to reduce variability.
• Very important point!!
– Middle paragraph, p. 90.
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HW
• Read Section 2.2 (pp. 82-98)
• Exercises:
– p. 86: 2.27-2.29
– p. 90: 2.30-2.32
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Do you lotto?
• Read paragraph in blue, pp. 82-83.
• From sample to population, p. 85
– We take a sample from a population, and use the statistic to estimate the parameter of interest.
• Population … parameter
• Sample … statistic
• Notations
– Means and proportions
15
Confidence Intervals andMargin of Error
16
What margin of error means (p. 92)
• http://www.gallup.com/poll/111949/US-Workers-Continue-See-Deteriorating-Job-Market.aspx
• Quick method for calculating margin of error:
nME /1
17
Confidence Statements
• We generally use “95% Confidence,” which means this:
– 95% of all confidence intervals constructed in the same manner will contain the true population parameter.
• 5% of the confidence intervals created will not contain the population parameter.
18
Important Notes
• See bulleted list, p. 96
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Exercises, p. 95
• 2.36, 2.37, 2.38, 2.39
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Practice
• Pages 97-98:
– 2.40-2.44
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Sampling from Large Populations
• As long as the population size (N) is at least 10X the size of the sample (n), the variability of a statistic from a random sample does not depend on the population size.
– See explanation, p. 98
• Exercise 2.46, p. 99
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Quiz, Sections 2.1-2.2 Tomorrow
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Section 2.3
• Handout– Random Sampling Errors
– Sampling Errors
– Non-sampling Errors
• Which type of error does your margin of error address?
• You must know this material!
24
Stratified Random Sample
• A stratified random sample is one obtained by separating the population elements into non-overlapping groups (called strata), and then selecting a simple random sample from each stratum.
• Reasons for choosing a stratified random sample:
– Estimates are often needed for the subgroups of the population.
– Focuses on important subpopulations but ignores irrelevant ones.
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At Asheville School …
• What strata might be important if you were surveying Asheville School?
26
Weighting the Strata
• Proportionate allocation uses a sampling fraction in each of the strata that is proportional to that of the total population. If the population consist of 60% in the male stratum and 40% in the female stratum, then the relative size of the two samples (one males, one females) should reflect this proportion.
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Practice Problems
• pp. 119-120: 2.69, 2.70
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What to ask before believing a poll …
• Bulleted list, p. 121
• Practice exercise 2.72
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Review Exercises, pp. 130-132
• 2.86, 2.88, 2.90, 2.93, 2.94
• Test on Thursday
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