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Chapter 2: Sampling and Surveys

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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?

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Simple Random Sample (SRS)

• Definition, p. 69

• Did we choose an SRS?

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Biased Sampling Methods (p. 66)

• Voluntary response methods

• Convenience sampling

• Exercises, pp. 67-68: 2.1, 2.4

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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

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Confidence Intervals andMargin of Error

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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

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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.

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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!

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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?

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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