1. Warm-up Page 230 #37-40 You will enter your answers into Socrative
Get ready for homework questions.

2. Other Sampling Methods
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.
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.
Sampling and Surveys
Definition:
To select a stratified random sample, first classify the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRSs to form the full sample.

3. Use the form on the Wiki page to input your 3 samples.
Activity: Sampling Sunflowers page 216
Use Table D or technology to take an SRS of 10 grid squares using the rows as strata. Then, repeat using the columns as strata.
Sampling and Surveys
Use the form on the Wiki page to input your 3 samples.

4. Page 228
20)
Label the 500 midsize accounts from 001 to 500, and the 4400 small accounts from 0001 to 4400.
Starting at line 115, the first three accounts in each stratum are 417, 494, and 322 for the midsize group, then 2470, 1893 and 3259 for the small group.

5. Other Sampling Methods (cont.)
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.
Sampling and Surveys
Definition:
To take a cluster sample, first divide the population into smaller groups. Ideally, these clusters should mirror the characteristics of the population. Then choose an SRS of the clusters. All individuals in the chosen clusters are included in the sample.

6. Page 228
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With an SRS, it would be possible to get a sample that was all water view.
We should use the different types of view as the strata, & randomly pick 60 guests from each stratum. This would assure the manager that he had received opinions from guests who stayed in each type of room.
b) Someone could just slip the forms under a specific pattern of doors. All rooms ending in a specific number would be the clusters – for example all rooms ending in 16. Presumably these are all stacked above each other on the 30 floors.
The manager should just pick 2 random numbers that represent rooms on the water side & 2 random numbers that represent rooms on the golf course side and then survey all 30 rooms (1 per floor) that end in each number.

7. Page 228
24)
The chance of being interviewed is 3/30 for students over age 21 and 2/20 for students under age 21. This example is 1/10 in both cases
It is not an SRS because not all combinations of students have an equal chance of being interviewed.
For instance, groups of 5 students all over age 21 have no chance of being interviewed.

8. Page 228
26)
28)
a) Split the 200 addresses into 5 groups of 40 each. Looking for 2-digit numbers from 01-40, the table gives 35, so the systematic random sample consists of 35, 75, 115, 155 & 195.
b) Every address has a 1 in 40 chance of being selected, but not every subset has an equal chance of being picked – for example, 01, 02, 03, 04 & 05 cannot be selected by this method.
This method will miss those who do not have telephones, thus we will be likely to under-represent the poor in our sample.

9. b) Nonsampling error – this is an example of a processing error.
Page 229
30)
a) Nonsampling error – people may lie in response to questions about past drug use. It is not an error due to the act of taking a sample; rather, it is a response error.
b) Nonsampling error – this is an example of a processing error.
c) Sampling error – this will suffer from the same forms of bias as any voluntary response survey.

10. Page 229
The higher no-answer rate was probably in the second period – when families are likely to be vacationing or spending time outdoors.
32)

12. Page 229
The higher no-answer rate was probably in the second period – when families are likely to be vacationing or spending time outdoors.
32)
A high rate of nonresponse makes sample results less reliable because you don’t know how these individuals would have responded.
It is very risky to assume that they would have responded exactly the same way as those individuals who did respond.

13. The question is so complicated that it isn’t clear.
Page 229
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People likely claim to wear their seat belts because they know they should; they are embarrassed or ashamed to say that they do not always wear seat belts. Such bias is likely in most surveys about seat belt use (and similar topics).
36)
a) The question is clear, but the two options presented are too extreme; no middle position on gun control is allowed.
The question is so complicated that it isn’t clear.
It is also slanted; the phrasing will tend to make people respond in favor of a nuclear freeze.
Only one side of the issue is presented.

14. 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.
Sampling and Surveys
Why should we rely on random sampling?
To eliminate 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.

15. Sample Surveys: What Can Go Wrong? Page 221
Most sample surveys are affected by errors in addition to sampling variability.
Good sampling technique includes the art of reducing all sources of error.
Sampling and Surveys
Definition
Undercoverage occurs when some groups in the population are left out of the process of choosing the sample.
Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to participate.
A systematic pattern of incorrect responses in a sample survey leads to response bias.
The wording of questions is the most important influence on the answers given to a sample survey.

16. Chapter 4 Designing Studies
4.1 Samples and Surveys
4.2 Experiments
4.3 Using Studies Wisely

17. Section 4.2 Experiments After this section, you should be able to…
Learning Objectives
After this section, you should be able to…
DISTINGUISH observational studies from experiments
DESCRIBE the language of experiments
APPLY the three principles of experimental design
DESIGN comparative experiments utilizing completely randomized designs and randomized block designs, including matched pairs design

18. Observational Study versus Experiment page 231
In contrast to observational studies, experiments don’t just observe individuals or ask them questions. They actively impose some treatment in order to measure the response.
Experiments
Definition:
An observational study observes individuals and measures variables of interest but does not attempt to influence the responses.
An experiment deliberately imposes some treatment on individuals to measure their responses.
When our goal is to understand cause and effect, experiments are the only source of fully convincing data.
The distinction between observational study and experiment is one of the most important in statistics.

19. Observational Study versus Experiment
Observational studies of the effect of one variable on another often fail because of confounding between the explanatory variable and one or more lurking variables.
Experiments
Definition:
A lurking variable is a variable that is not among the explanatory or response variables in a study but that may influence the response variable.
Confounding occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.
Well-designed experiments take steps to avoid confounding.

20. The Language of Experiments page 233
An experiment is a statistical study in which we actually do something (a treatment) to people, animals, or objects (the experimental units) to observe the response. Here is the basic vocabulary of experiments.
Experiments
Definition:
A specific condition applied to the individuals in an experiment is called a treatment. If an experiment has several explanatory variables, a treatment is a combination of specific values of these variables.
The experimental units are the smallest collection of individuals to which treatments are applied. When the units are human beings, they often are called subjects.
Sometimes, the explanatory variables in an experiment are called factors. Many experiments study the joint effects of several factors. In such an experiment, each treatment is formed by combining a specific value (often called a level) of each of the factors.

21. Response variable – adult ratings of their behavior
Pg 253 #46
a) observational study – no treatment was imposed on the children. The researchers simply followed them through their 6th year in school, asking adults to rate their behavior at several times along the way.
Experiments
Explanatory variable – amount of time in child care from birth to age 4 ½ .
Response variable – adult ratings of their behavior
c) no. This study is an observational study, so we cannot make a conclusion about cause and effect. There could be a lurking variable that is actually causing the difference in adult ratings of their behavior.

22. Answers may vary. Level of academic motivation.
Pg 253 #48
a) observational study – the researchers did not assign people to either use or not use cell phones.
Experiments
b) no. This study is an observational study, so we cannot make a conclusion about cause and effect.
Answers may vary. Level of academic motivation.
Those who drink may have less academic motivation, leading to lower grades.
So if students do not do well, we are not sure if it is because of the alcohol itself or because of lower level of academic motivation.

23. Subjects: the students living in the selected dormitory
Pg #52
Subjects: the students living in the selected dormitory
Explanatory variable: the rate structure.
Treatments: paying one flat rate or paying peak/off-peak rates
Response variables: the amount and time of use and total network use.
Experiments

24. Subjects: middle schools
Pg 254 #54
Subjects: middle schools
Explanatory variable: physical activity program offered and nutrition program offered
Treatments: activity intervention
2. nutrition intervention
3. both interventions
4. neither intervention
Response variables: physical activity and lunchtime consumption of fat
Experiments

25. Read pg
Do pg 227 #21-35 odd
Do pg 253 #45-49 odd
Reading Guide Section 4.2 #1-16
Chapter 4 Vocabulary Flash Cards
Estimated Test Date is Friday, February 12.