Algebra 1 Glencoe McGraw-Hill JoAnn Evans

Math 8H

12-1Sampling and Bias

A random sample is a set of items that are chosen from a population in such a way that each time an item is selected,

every item in the population has an equal opportunity to appear in the sample.

A random sample must be representative of the population

and chosen without preference.

Type Definition Example

Simple

Random

Sample

Stratified

Random Sample

Systematic

Random

Sample

A simple random sample is a sample that is as equally likely to be

chosen as any other sample from the

population.

A population is first divided into similar,

non-overlapping groups. A simple random sample is chosen from each

group.Items are selected at specified times or intervals from the

population.

150 passengers on an airplane are each

assigned a different number from 1-150.

Five of the 150 numbers are chosen at random to get a free flight coupon.150 passengers are

divided into 2 groups by gender. Two passengers are

randomly selected from each of the two groups to get a free

flight coupon.

Every 30th passenger to board the plane is

given a free flight coupon.

Ten students are going to be chosen from each class at Thousand Oaks High School to be on an advisory

committee with the principal.

What is the sample?

The sample is 4 groups of 10 students: 10 freshman, 10 sophomores, 10 juniors, and 10 seniors.

What is the population in this case?

The population is the entire student body of TOHS.

This is a stratified random sample. The population is divided into non-overlapping groups, then a random sample will be chosen from each group.

A clothing company wanted to check the quality of the jeans it produced. Instead of inspecting each and

every pair of jeans, the manager decided to inspect every fourth pair that was produced.

What is the sample?

The sample is every 4th pair of jeans that is produced.

What is the population in this case?

The population is the jeans made by the company.

This is a systematic random sample. The population of jeans to be chosen will be at regular intervals (every 4th pair that is made).

Mrs. Lowe chooses students to pass out snacks each day in her kindergarten class. Each of her 20 students’ names are written on a small piece of paper, placed in

a cup, and mixed up. She pulls out 4 names to be snack helpers.

What is the sample?

The sample is four students.

What is the population in this case?

The population is Mrs. Lowe’s kindergarten class.

This is a simple random sample. Each student is equally likely to be chosen as a snack helper for the day.

Biased vs. Unbiased Samples

Remember, a random sample is considered to be representative of the entire population it’s drawn

from and is chosen without any preference (favor).

A random sample is considered, therefore, to be unbiased. It is impartial and without favoritism.

In contrast, a biased sample will favor one or more parts of the chosen

population over others.

A hospital’s administration is interested in opening a gym for all its employees. They ask each

member of the night-shift emergency room staff if he or she would use a gym, and if so, what hours

the employees would prefer to use it.

Sample? The night-shift staff of the hospital

Population?

All hospital employees

Biased? Unbiased? Why?

Biased; Since they all work the night shift, their idea of hours the gym should be open will be hours convenient for their schedule.

Every tenth customer in line at the Human Bean Coffee Shop is asked what their favorite beverage

is.

Sample? Every 10th customer

Population?

All customers of the Human Bean

Biased? Unbiased? Why?

Biased; Customers who go to this coffee shop may be biased in favor of the drinks sold there.

Simple? Stratified? Systematic?

Systematic; customers were chosen at a given interval (every 10th one).

T o determine the number of students who use computers to do their homework, the middle

school office chooses 10 students at random from each grade and then interviews the students.

Sample? 10 6th, 10 7th, and 10 8th grade students

Population?

All students in the school

Biased? Unbiased? Why?

Unbiased

Simple? Stratified? Systematic?

Stratified; students were chosen from similar, non-overlapping groups.

Type Definition Example

Popular Forms of Samples That Can Be Biased

Convenience

Convenient means EASY; a convenience sample will consist of

members that are easily accessible.

The HS administration wanted to evaluate how homecoming week was

conducted at school. Every female member of the ASB class was asked how she

liked the activities that week. It was convenient to

sample the students in just one class.Voluntary

ResponseA voluntary

response sample will only include members who

want to participate in the sampling.

Paper surveys are sent home for the parents of 8th

graders to ask their opinions about the

homework policy. This is voluntary because only those who choose to do the survey will return it.

To find out more about the music preferences of their customers, the owners of a music store

asked 20 customers who expressed interest to participate in an in-store interview. During the

interview they listened to new CDs from artists in all music categories.

Sample? 20 customers of the music store

Population?

All customers of the music store

Convenience or Voluntary Response Sample?

Voluntary Response; only the opinions of those customers who were interested in doing an interview about music preferences were sampled

During the April meeting, the president of the PTSA asked 6 parents and 6 teachers for their opinions on whether the 8th grade promotion

dance should be held the week before promotion or the night after promotion.

Sample? 6 parents and 6 teachers

Population?

All parents and teachers of the school

Convenience or Voluntary Response Sample?

Convenience; it was handy to ask their opinions since they were all in one place

Simple random

Systematic random

Stratified random

Convenience

Voluntary Response

Identify the Sample

Sonia has been asked to determine whether the students at her school think there should be any “A” period classes next year. She asks 20 of her friends who are in her 7th

grade “A” period math class. 17 of them said they thought there should be “A” period classes. Sonia reported that

85% of students polled supported the idea of having early classes next year.

Sample? 20 students in Sonia’s “A” period math class

Population?

All students in the school

Biased or Unbiased?

Classify

Biased sample—only those already taking a class were sampled

Convenience Sample

Identify the Sample

A shoe manufacturer wants to check the quality of the shoes produced by its employees. Every 15 minutes, five pairs of shoes are pulled off the assembly line to have a

careful inspection for quality.

Sample? 5 pairs of shoes, every 15 minutes

Population?

All shoes on the assembly line

Biased or Unbiased?

Classify

Unbiased sample

Systematic random sample

Practice Problems—Write Your Responses to the Questions

1. The owners of a mall want to know if they should put a movie theater in the mall. Every hour, the mall manager questions 20 of the people coming into the mall.

What is the sample?

What is the population?

Is the sample simple, stratified, or systematic?

2. A sub sandwich store owner wants to make sure that his employees are correctly weighing the meat that is put on the sandwiches. He watches an employee weigh the meat for one hour.Is the sample biased or unbiased?

3. A fast food restaurant is testing a new food item. To test if the customers are satisfied, the store owner asks the first 15 customers of the day if they would purchase the item.

What is the sample?

What is the population?

Is it a convenience or a voluntary response

sample?

4. A state tourism board wants to determine the state’s favorite camping site. They send a survey to all mailing addresses in the state to be filled out and mailed back to them.

What is the sample?

What is the population?

Is the sample unbiased or biased?

• If unbiased, classify it as simple, stratified,

or systematic.

• If biased, classify it as convenience or

voluntary response.

Answers:

1.Sample: a group of shoppers at the mall, 20 every hour

Population: all mall shoppersSystematic random sample: people are chosen

according to a given time interval

2.Biased: he’s only watching one employee for one hour

3.Sample: first 15 customers of the dayPopulation: all the customers of the restaurant

4.Sample: people in the state with a mailing addressPopulation: all the people in the stateBiased: only residents will be surveyedVoluntary response: only those who want will

mail their response