1 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 : 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

6 Calculator Corner, p. 73 “Random” digits

7 HW Reading: Section 2.1, pp Exercises, pp : –2.17, 2.19, 2.22, 2.23, 2.24

8 Do you lotto? Read paragraph in blue, pp 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

9 Practice Exercises p. 86 –2.25, 2.26

10 Activity 2.2, p. 83

11 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)

12 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.

13 HW Read Section 2.2 (pp ) Exercises: –p. 86: –p. 90:

14 Do you lotto? Read paragraph in blue, pp 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 and Margin of Error

16 What margin of error means (p. 92) Continue-See-Deteriorating-Job-Market.aspxhttp:// Continue-See-Deteriorating-Job-Market.aspx Quick method for calculating margin of error:

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

19 Exercises, p , 2.37, 2.38, 2.39

20 Practice Pages 97-98: –

21 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

22 Quiz, Sections Tomorrow

23 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.

25 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.

27 Practice Problems pp : 2.69, 2.70

28 What to ask before believing a poll … Bulleted list, p. 121 Practice exercise 2.72

29 Review Exercises, pp , 2.88, 2.90, 2.93, 2.94 Test on Thursday