1. Federalist Papers Activity
Choose 5 words, find average length, class dotplot #####, STO, rand plants a “seed” Demonstrate randInt process Use randInt to choose 5 words and find avg length How do the dotplots compare? Why do you think they are different? Which do you think is more accurate? Actual average is 4.9

2. CHAPTER 4 Designing Studies
4.1
Samples and Surveys

3. Samples and Surveys
IDENTIFY the population and sample in a statistical study.
IDENTIFY voluntary response samples and convenience samples. EXPLAIN how these sampling methods can lead to bias.
DESCRIBE how to obtain a random sample using slips of paper or technology.
DISTINGUISH a simple random sample from a stratified random sample or cluster sample. Give the advantages and disadvantages of each sampling method.

4. Population, Census, and Sample
The population in a statistical study is the entire group of individuals we want information about.
A census collects data from every individual in the population.
A sample is a subset of individuals in the population from which we actually collect data.
Population
Collect data from a representative Sample...
The distinction between population and sample is basic to statistics. To make sense of any sample result, you must know what population the sample represents
Sample
Make an Inference about the Population.

5. Problem: Identify the population and sample in each of the following settings.
(a) The student government at a high school surveys 100 students at the school to get their opinions about a change to the bell schedule.
(b) The quality control manager at a bottling company selects a sample of 10 cans from the production line every hour to see whether the volume of the soda is within acceptable limits.

6. The Idea of a Sample Survey
We often draw conclusions about a whole population on the basis of a sample. Choosing a sample from a large, varied population is not that easy.
Choosing a Sample
Step 1: Define the exact population we want to describe.
Step 2: Say exactly what we want to measure.
A “sample survey” is a study that uses an organized plan to choose a sample that represents some specific population.
Step 3: Decide how to choose a sample from the population.

7. Current Population Survey (pg. 211)
Define the population for this survey.
What makes up the sample in this survey?
How can someone be considered not in the labor force? Why do you think they include this category for this survey?

8. How to Sample Badly
How can we choose a sample that we can trust to represent the population? There are a number of different methods to select samples.
Choosing individuals from the population who are easy to reach results in a convenience sample. (Examples?)
Convenience samples often produce unrepresentative data…why?
The design of a statistical study shows bias if it would consistently underestimate or consistently overestimate the value you want to know.

9. How to Sample Badly
Convenience samples are almost guaranteed to show bias. So are voluntary response samples, in which people decide whether to join the sample in response to an open invitation.
A voluntary response sample consists of people who choose themselves by responding to a general invitation. (Examples?)
Voluntary response samples show bias because people with strong opinions (often in the same direction) are most likely to respond.
Bias is not the result of bad luck. It is the result of a poorly designed study.

10. Pg. 213 Example (Try not to look at the solution)
Pg. 213 Check Your Understanding

11. How to Sample Well: Simple Random Sampling
A sample chosen by chance rules out both favoritism by the sampler and self-selection by respondents. Random sampling involves using a chance process to determine which members of a population are included in the sample.
A simple random sample (SRS) of size n is chosen in such a way that every group of n individuals in the population has an equal chance to be selected as the sample.
How could we randomly select 4 students from our class?
In practice, people often use random numbers generated by a computer or calculator to choose samples.

12. We already did this on the Federalist Papers Activity
How to Choose an SRS
Choosing an SRS With Technology
Step 1: Label. Give each individual in the population a distinct numerical label from 1 to N.
Step 2: Randomize. Use a random number generator to obtain n different integers from 1 to N.
We already did this on the Federalist Papers Activity

13. Stratified Random Sample
The basic idea of sampling is straightforward: take an SRS from the population and use your sample results to gain information about the population.
Sometimes there are statistical advantages to using more complex sampling methods.
To get a stratified random sample, start by classifying the population into groups of similar individuals, called strata.
Then choose a separate SRS in each stratum and combine these SRSs to form the sample.
One common alternative to an SRS involves sampling important groups (called strata) within the population separately. These “sub-samples” are combined to form one stratified random sample.

14. Sampling Sunflowers Activity (pp. 219-220)
Handout Activity Worksheet
Stratified random sampling works best when individuals within a strata are similar and there are large differences between strata.
Congress is proposing a massive overall to the Social Security program. What might be a good variable to stratify the population? What wouldn’t be a good variable?
How might you stratify students at the high school for a study?

15. Cluster Sample
Although a stratified random sample can sometimes give more precise information about a population than an SRS, both sampling methods are hard to use when populations are large and spread out over a wide area.
In that situation, we’d prefer a method that selects groups of individuals that are “near” one another.
To get a cluster sample, start by classifying the population into groups of individuals that are located near each other, called clusters.
Then choose an SRS of the clusters. All individuals in the chosen clusters are included in the sample.
One common alternative to an SRS involves sampling important groups (called strata) within the population separately. These “sub-samples” are combined to form one stratified random sample.

16. Cluster Sample
Cluster sampling works best when a cluster looks just like the population but on a smaller scale.
Strata sampling divides the population into strata and takes “some from all”
Cluster sampling divides the population into clusters and takes “all from some”
How might a cluster sample work at our high school?

17. Samples and Surveys
IDENTIFY the population and sample in a statistical study.
IDENTIFY voluntary response samples and convenience samples. EXPLAIN how these sampling methods can lead to bias.
DESCRIBE how to obtain a random sample using slips of paper, technology, or a table of random digits.
DISTINGUISH a simple random sample from a stratified random sample or cluster sample. Give the advantages and disadvantages of each sampling method.

18. Sec. 4.1 Assignment
Pg. 229 #1,3,5,7,9,13,17b-c,21,25

19. Inference for Sampling
The purpose of a sample is to give us information about a larger population.
The process of drawing conclusions about a population on the basis of sample data is called inference.
Why should we rely on random sampling?
To avoid bias in selecting samples from the list of available individuals.
The laws of probability allow trustworthy inference about the population
Results from random samples come with a margin of error that sets bounds on the size of the likely error.
Larger random samples give better information about the population than smaller samples.

20. Sample Surveys: What Can Go Wrong?
Most sample surveys are affected by errors in addition to sampling variability.
Good sampling technique includes the art of reducing all sources of error.
Undercoverage occurs when some members of the population cannot be chosen in a sample.
Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to participate. (How is this different from voluntary response?)
A systematic pattern of incorrect responses in a sample survey leads to response bias. (Comic pg. 227)
The wording of questions is the most important influence on the answers given to a sample survey. (Holocaust Poll Example)

21. Gallup Poll Exercise
We constantly hear poll results reported in the media and Gallup polls are one of the most common
In this exercise you will learn some key components about Gallup polls including how they are conducted, what sample size they use, and how reliable they are
May work with a partner (Each individual will turn in assignment)
Read over the Information Sheet provided (Gallup FAQs)
Answer the questions from the worksheet
Answer questions from book pg. 233 #27,29,35,37