Chapter 5 Sampling and Surveys5.1 Samples, Good and Bad

Bias• Design flaw of a statistical study that systematically favors

certain outcomes.

• Systematically favoring one outcome over another

Samples•Sample is a small group from a larger

population.•Representative samples have the same

characteristics of the larger population

BIASED SAMPLES:Voluntary Response Sample

• Individuals choose to become part of the sample by responding to a general request.

•Very biased in that many reply with extreme or strong opinions on the subject matter.

•Not a representative sample since not all people would choose to respond.▫EX: Call-in, write-in, asking people at the

mall to stop, etc.

Convenience Sample

•Selection of individuals that are easily obtained. •Biased•Not a representative sample.

Practice: p. 205 #2-4

5.2 An online poll(a) Voluntary Response Sample(b) The sample is limited to those that read Parade, those that have access to online services, and were willing to go to the website to vote. The 85% is probably higher than the true percent of all adults who believe that cell phone use while driving should be banned. People that are for the ban on cell phones would probably have stronger feelings on the subject and be more likely to go online to complete the survey.

5.3 Sleepless nights(a) Convenience Sample(b) Since the student chose the first 100 to arrive these students had probably had a good night sleep, awoken refreshed, and made it to school early. The average is probably higher than the true average since those that did not sleep well or went to bed late probably hadn’t made it to school yet. 5.4 Hand-washing habits(a) When asked the question most people would not admit to not washing their hands. (b) The observers did not want to bias the study by letting the people be aware of being watched. If the people knew they were being studied they might behave in a different manner.

Unbiased SampleSimple Random Sample (SRS)•Sample of size n from a population chosen in

such a way that:1. Every individual of the population has the

same chance of being selected2. Every possible sample of size n has the same

chance of being selected.

Example: 4 Students need to be selected to represent the class in Statistics Conference in Cancun during Spring Break.

1. Put everyone’s name in hat, mix it up, and select 4 names.

2. Put all the boy’s names in one hat and all the girl’s names in a second hat. Randomly select 2 boys and 2 girls.

How to take a SRS:

Table of Random Digits (table A)-

• A long string of digits (0-9) with the following properties:

• Each digit in the table is equally likely to be any of the 10 digits

• The entries are independent of each other. So knowing one digit doesn’t affect what the next one is.

How to write instructions for SRS:

• Label each _______ with #__ -- __

• Use TRD, read across, every ____ digits represent a ______.

• Ignore #’s ________, and repeats

• The first _____ numbers are our sample

HOW TO USE THE TABLE (p.T2):

* Label each individual in your population with a number

* Each number given must have the same number of digits

2) TABLE* Go to the table and read across

in groups that are the same size as the numbers you assigned your individuals

1) LABEL

EXAMPLE:Take a sample 5 from the following list. Start at line 131 in the table.

Smith Jones Holloway

DeNizzo David Adams

Schaefer Gray Capito

Meyers Gingrich Card

Dietrich Moreland Hall

Walsh Whitter Jordan

Instructions

1. Assign 01-18 to each of the subjects and ignore 19-99,002. Use TRD and read off 2 digits at a time3. Read off 5 numbers ignoring any repeats.

05007 16632 81194 14873 04197 85576 45195

96565 68732 55259 84292 08796 43165 93739

31685 97150 45740 41807 65561 33302 07051

Practice - p. 209 #5.7 - 5.97. Apartment LivingInstructions:1. Use a TRD and read off 2 digits at a time2. Let 01-33 each be an apartment complex

Ignore 00,34-993. Read off 3 numbers ignoring repeats

Line 117:

38167 98532 62183

8. How do random digits behave?(a) False(b) True(c) False

9. An election day sample(a) Instructions:1. Use TRD and read off 3 digits at a time2. Let 001-440 each be a precinct and ignore 000, 441-9993. Read off 25 numbers ignoring repeats

82739 57890 20807 47511 81676 55300 94383 14893

60940 72024 17868 24943 61790 90656 87964 18883

36009 19365 15412 39638 85453 46816 83485 41979

Random Sampling on the Calculator