And You Believed That?! (Learning Task)

Solutions

What claim is being made? What is special about the claim?

• The claim being made is that college students that use Facebook will have lower grades or that college students with lower grades use Facebook.

• Does one thing cause another?

Bias in Questions • “Is it really possible for a person to still believe

that wearing a seat belt is not completely necessary?”

• “Is wearing a seat belt necessary for the complete safety of all passengers?”

• “Wearing a seat belt is currently required by state law. Do you agree with this law?”

How could anyone be this dumb?

Complete Safety?

What are you an outlaw?

4. Determine whether each study below has a source of bias. If there is a source of bias, describe the bias and why this bias makes the sample unrepresentative.

a) A medical company uses sick patients to test their competitors’ drugs for side effects

There is a sampling bias because the entire population does not have an equal chance or representation in the sample

4 b) A medical company uses healthy patients to test their competitors’ drugs for side effects

• There is a sampling bias because the entire population does not have an equal chance or representation in the sample

c) A newspaper polls 9th grade students to measure if students are going into the Armed Forces after high school

• This study has a sample bias. 12th graders are not represented in the study and it is reasonable to suppose that 12th graders have different opinions than freshmen.

d) The Department of Education conducts and online poll that asks “Do you have internet service at home?”

• This study has a sample bias. You are asking people who are online if they are online

• …duh.

e) A survey is mailed to voters in Augusta asking “Will you vote for the one cent sales tax increase in Augusta?” There is no bias in this study

• This survey will have a response bias. People with a strong interest in taxes are more likely to respond than disinterested parties.

• So those with a strong interest are overrepresented.

f) A survey is mailed to voters in Augusta who make more than $90,000 a year asking “Will you vote for the one cent sales tax increase in Augusta?”

• This survey will have a response bias. People with a strong interest in taxes are more likely to respond than disinterested parties.

• Also this study has a sample bias, people making less than $90,000 are not represented at all.

5. For each experiment, determine which sampling technique would be most appropriate. Then explain how you would obtain a sample and why the technique you chose was appropriate. a) A company wants to decide who likes wheat bread more, men or women

• stratified random sampling – divide the population into two groups, men and women, and randomly select from each group

b) A newspaper wants to determine which areas of town have the least number of subscriptions

• stratified random or cluster – divide the population into groups according to their geographic location (north, south, east, west) then randomly select from each group

c) You want to estimate the number of people in your school who are vegans.

• Simple random or systematic sampling – assign each student a number then randomly generate a sample of students

d) You want to determine whether 9th graders or 12th graders are more likely to be vegans.

• Stratified random sampling – divide population into two groups, 9th and 12th graders, then randomly select from each group

Vegans are not

nice.

e) The Department of Children Services wants to count the number of homeless children in a city. They only have enough counters to cover one-sixth of the city.

• cluster sampling- divide town into six group then select one of the groups

f) A manufacturer wants to test the taste of their frozen vegetables as the bags of vegetables come out of a freezer.

• Simple random sample – randomly choose bags of vegetables from different locations in the freezer

6. Referring to the article “Facebook use linked to less textbook time,” what type of sampling technique do you believe the researchers may have used? Why?

• Some type of convenience sampling

Emma

7. Consider the student body of your high school to be the population for a study being conducted by the school newspaper. One of the newspaper students, Emma, is writing an article on study habits. She has carefully designed a survey of five questions. Is it reasonable to think that she can survey the entire student body?

Nope

8. Emma has decided to survey 50 students. For the following, explain how she could select each type of sample from the students at your school.

Simple:

• List all of the students in alphabetical order and then number the students from 1 -2200.

• Use a random number to select 50 numbers at random between 0 and 2201.

Systematic:

• Divide 2200 by 50 = 44

• Select a random number between 0 and 45 inclusive.

• Then count up by 44 until you have 50 numbers

• For example if 27 were then seed then 27 71 115 159 203 247 291 335 379

423 467 511 555 599 643 …

• Now select these subjects from your alphabetized list

Stratified:

• Do a Simple Random Sample from the freshman class. Include 25 subjects

• Do a Simple Random Sample from the sophomore class. Include 25 subjects

• Do a Simple Random Sample from the Junior class. Include 25 subjects

• Do a Simple Random Sample from the Senior class. Include 25 subjects

Cluster

• Identify subgroups of the student body – Band

– DECA

– Football team

• Calculate what percentage of the population each cluster is

• Draw from that cluster a portion of the sample in proportion to the percentage that cluster represents.

9. Another student on the staff thinks that Emma is making the assignment too difficult and suggested that she simply survey the students in her first period class. Would this be an appropriate sampling method? Explain.

• This convenience sample method is not the best because it may over represent.

– Smart people (cause Emma takes AP)

– People who show up to school on time

– Emma’s crew

• Considering budget this may be the best method available.