This weekend please complete the "Chapter 12 Homework: Identifying Sampling Methods" worksheet provided in class (or below).
- Answers are posted in green below--check!
- On Monday/Tuesday in class we will continue to discuss sampling, sampling methods, and examine population parameters vs. sample statistics
- The seven sampling methods we saw today are seven new vocab words for chapter 12!
- This homework assignment extends our learning from today's classwork...
- Use the notes/definitions provided in today's investigation to help with your homework.
- See below for an example of a procedure for each sampling method using a different context (you'll get a paper copy of this on Monday).
Here are some examples of procedures for each sampling method using a different context:
Simple Random Sample:
Context: The town of East Hartford is interested in
surveying its adult (age 18+) residents about various topics. You
have been hired to choose a sample of 500 East Hartford residents to be
surveyed.
Example:
1.
Number
each EH adult resident from 1 to _____.
2.
Use
a random number generator to generate 500 numbers between 1 and____, ignoring
repeated numbers.
3.
Survey
the 500 adult EH residents whose numbers were randomly selected.
Census
Context: The town of East Hartford is interested in
surveying its adult (age 18+) residents about various topics. You
have been hired to choose a sample of 500 East Hartford residents to be
surveyed.
Example: Mail each adult resident (age 18+)
in the town of East Hartford a survey asking questions about the desired
topics, and ask each person to complete the survey questions and return the
form. You may also provide a link to an online version of the survey for people
to complete.
For those
residents who do not complete the survey (by mail or online), follow up with a
phone call. For those who still do not respond, send a town official
door-to-door to collect survey responses from the remaining adult EH residents.
Stratified Random Sample
Context: The town of East Hartford is interested in
surveying its adult (age 18+) residents about various topics. You
have been hired to choose a sample of 500 East Hartford residents to be
surveyed.
Example: You believe that people’s
responses to these questions may differ by age group; therefore, you first
separate all EH residents into groups based on age (stratify).
1.
First,
you create (5) groups of residents ages 18-30, 31-45, 46-60, 60-75, and 75+.
(This means we stratified by age group).
2.
Next,
we use a random number generator to randomly generate the social security
numbers of 100 residents within the 18-24 age group. Ignore any repeated
numbers.
3.
We
then survey these randomly selected residents by mail (also providing a link to
an online survey), then by phone (if they do not respond initially).
4.
Repeat
this process for each age group, randomly generating social security numbers
(ignoring repeats) to select a random sample from each strata.
*Note:
with a stratified sampling method we do not always want to sample the same number
from each strata; instead, we want to sample in proportion to our population
·
For
example, if 50% of the adult residents in EH were ages 46-60, we would want 50%
of our sample to be taken from this age group…
·
We
will discuss this more moving forward.
Cluster Random Sample
Context: The town of East Hartford is interested in surveying its adult
(age 18+) residents about various topics. You have been hired to choose a
sample of 500 East Hartford residents to be surveyed.
Context: The town of East Hartford is interested in
surveying its adult (age 18+) residents about various topics. You
have been hired to choose a sample of 500 East Hartford residents to be
surveyed.
Example:
1.
First,
separate the town into groups (clusters) by elementary school district. (each
school district = 1 cluster)
2.
Next,
number each school district from 1-8.
3.
Use
a random number generator to randomly select two numbers from 1-8, ignoring
repeats.
4.
Survey
all of the adult residents (age 18+) within those two randomly selected
districts.
Systematic Random Sample
Context: The town of East Hartford is interested in
surveying its adult (age 18+) residents about various topics. You
have been hired to choose a sample of 500 East Hartford residents to be
surveyed.
Example:
1.
Obtain
a list of the names of all adult EH residents. List each resident in
alphabetical order, by last name.
2.
Number
each person on the list from 1 - ___.
3.
Generate
a random number to represent your starting point. Survey the resident with that
number.
4.
Now,
survey every 10th person on this list starting from the random
number generated above.
Voluntary Response Sample
Context: The town of East Hartford is interested in
surveying its adult (age 18+) residents about various topics. You
have been hired to choose a sample of 500 East Hartford residents to be
surveyed.
Example:
1.
Create
an online survey (poll) and post it on the town’s website and each of the
school websites.
2.
Mail
a letter to each household to make all residents aware that the survey has been
posted.
3.
Collect
responses (data) from anyone who chooses to go online and complete the survey.
Convenience Sample
Context: The town of East Hartford is interested in
surveying its adult (age 18+) residents about various topics. You
have been hired to choose a sample of 500 East Hartford residents to be
surveyed.
Example:
1.
Have
multiple town officials go to various neighborhoods throughout East Hartford
with copies of the survey.
2.
Have
these officials administer the survey to any residents who are available or
passing by.
OR
1.
The
people conducting the study provide the survey to their friends and family and
ask them to complete it.
2.
To
obtain more data, they stand outside the town hall and/or public library and
hand out surveys to those passing by.
And here are the homework answers so you can check:
11a.) Voluntary Response Sample
11b.) Cluster sample
11c.) (Attempted) Census
11d.) Stratified Survey
11e.) SRS (Simple Random Sample)
12a.) Convenience OR Voluntary Response Sample
12b.) Voluntary Response Sample
12c.) Cluster Sample (Maybe stratified by elementary school, then cluster choosing class = multistage)
12d.) Systematic Sample
12e.) Stratified Sample
13a.) Used a combination of stratifying and cluster; first separated into groups (churches) and randomly selected 3 churches (this is a cluster approach), but then selected 100 people from each of these selected churches (stratified approach)--we call this a multi-stage sample
13b.) The 100 members chosen from the 3 randomly selected churches may not be representative of all Catholic church members in this city.
15a.) Systematic Sample
15b.) This sampple is not likely to be representative of how patrons feel about this ride because every person sampled is in line for this ride, and thus they likely have different opinions about having to wait in line than people who are not riding this ride. This sample is biased, as people willing to wait in line may be overrepresented.
27a.) Simple Random Sample:
- Number the transactions from 1-120.
- Use a random number generator to generate 10 numbers between 1 and 120.
- The supervisor then re-checks the 10 payments with the numbers that were randomly generated.
27b.) I would stratify (by type of sale, wholesale/retail).
- Number the wholesale sales from 1-36.
- Use a random number generator to generate 3 numbers in this range and then re-check these 3 transaction.
- *We choose 3 because we are told 30% of the overall sales are wholesale, so we want 30%, or 3 out of 10, of the sales in our sample to be wholesale so that our sample best represents our population
- Number the retail sales from 1-84.
- Use a random number generator to generate 7 numbers in this range and re-check these 7 retail transactions.
Also, don't forget to reflect and complete the extra credit assignment below--due Monday!
Extra Credit Homework Assignment: Midterm Exam Reflection Questions:
- These questions can be completed and turned in Monday for EXTRA CREDIT (homework and 2 or 3 stamps).
- You must write the question OR write the heading bulleted below each question
- No question/heading written, no extra credit
- This will be scored based on you showing real, thoughtful reflection--lazy, quick, one word answers for questions 3-8 will not earn extra credit! Take some time to truly reflect on your exam and on your first semester!
- Examine your score, the histogram, and summary statistics below to answer each question:
1. Record your projected AP score and your raw score below. (You will have to read the information on the blog to determine these).
- Projected AP Score:________ Raw Score:_______%
2. Calculate the z-score for your raw score using the data above. Show your work below.
3. What are your initial reactions to your individual exam score? Record at least three thoughts in the space below.
- Initial Reactions: Individual Score
4. Examine the data above; what are two positive things that stand out to you about our overall midterm exam performance?
- 2 Positives: Overall Performance
5. What is something that stands out as an area (or two) for improvement for our overall performance (as a whole group)?
- Area to Improve: Overall Performance
6. What are two things you have done well individually in preparing for success in AP Stat over the course of the first semester?
- Individual Preparation: 2 Successes
7. What are two things you can improve upon (moving forward) to put yourself in the best position to succeed on the AP exam in May?
- Individual Preparation: Areas to Improve
8. What are two things you learned from the midterm exam that will help you to better prepare for the AP exam (May 17)?
- Midterm to AP Exam: Takeaways
