Download Math 150 - El Camino College Compton Center

Math 150
Chapter 1 Notes
Mr. Martinez
Definitions:
 Data is collections of observations (such as measurements, genders, survey responses)
 Statistics is the science of planning studies and experiments, obtaining data, and then organizing, summarizing,
presenting, analyzing, interpreting, and drawing conclusions based on the data
 Population is the complete collection of all individuals (scores, people, measurements, and so on) to be studied;
the collection is complete in the sense that it includes all of the individuals to be studied
 Census is the collection of data from every member of a population
 Sample is the Subcollection of members selected from a population
Example: The researchers at a hearing research center want to know if the music played during the aerobics classes at
health clubs is loud enough to cause hearing damage. They randomly choose 10 health clubs from the 150 health clubs
in the area and measure the loudness of the music played during the aerobic classes.
A) What is the population?
B) What is the sample?
Solution:
A) The population is the aerobics classes at the health clubs.
B) The sample is the aerobic classes at the 10 randomly chosen health clubs.
Types of Samples
•
•
•
•
•
(Simple) Random Sample: Members are chosen using a method that gives everyone an equally likely chance of
being selected.
Systematic Sample: Members are chosen using a pattern, such as selecting every k-th person.
Stratified Sample: The population is first divided into groups. Then some members are randomly chosen from
each subgroup.
Cluster Sample: divide the population area into sections (or clusters); randomly select some of those clusters.
Choose all members from selected clusters.
Convenience Sample: Members are chosen because they are easily accessible.
Example: The officials of the National Football League (NFL) want to know how the players feel about some proposed
changes to the NFL rules. They decide to ask a sample of 100 players. Classify the sample:
A) The officials use a roster with the name of all the players in the league. Then, they select every 10th player.
B) The officials randomly choose 3 players from each of the 32 teams in the NFL.
C) The officials have a computer generated a list of 100 players from a database that includes all of the players in
the NFL.
Solution:
1
Math 150
Mr. Martinez
A) Systematic
B) Stratified
C) Simple random
Biased Samples
In a random sample, each person or object has an equally likely chance of being selected. A random sample is most
likely to produce a sample that is representative of a population. A non-random sample can result in a biased sample. A
Biased Sample is a sample that is not representative of a population. In a biased sample, the population can be
underrepresented or overrepresented.
•
•
Underrepresented: One or more parts of a population are left out when choosing the sample.
Overrepresented: A greater emphasis is placed on a one or more of the parts of a population when choosing
the sample.
Simple random, systematic, and stratified and cluster samples are preferred types of samples because the resulting
samples are usually random. The results of a convenience sample are more likely to be biased.
Example: Administrators at your college want to know if more vegetarian items should be added to the lunch menu.
Decide whether the sampling method could result in a biased sample. Explain your reasoning.
A. Survey every 10th student waiting in line to purchase lunch.
B. Survey every 25th student who enters the cafeteria during the lunch period.
Solution:
A. This method could result in a biased sample because it underrepresents the students who do not purchase
lunch. Some of these students may not purchase lunch because there are not enough vegetarian items on the
lunch menu.
B. This method is not likely to result in a biased sample because a wide range of students will be surveyed.
Example: A survey conducted by a city newspaper asks whether the use of hand-held cellular phones while driving in
the city should be banned. The question and results are the following:
Question: “Should using a hand-held cellular phone while driving be banned?”
Results from a survey of 1000 cellular phone users, 25% said Yes and 75% said No.
A. Tell why the results may be biased.
B. Suggest a way to eliminate the bias.
Solution:
A. The sample contains only cellular phone users, so cellular phone users are overrepresented.
B. The survey should be conducted using a random sample. For example, survey 100 randomly chosen people at 10
locations in the city.
2
Math 150
Mr. Martinez
When conducting a survey, it is important that the survey questions are carefully written. If a question is poorly written,
then the responses of the people surveyed may not accurately reflect their options or actions. These types of questions
are called biased questions. Some characteristics of biased questions are listed below.
•
•
•
The responder is encouraged or pressured to answer in a particular way.
The respondent is not provided enough information to give an accurate opinion.
The order in which the questions are asked may also introduce bias.
Example: Tell whether the questions may be biased. Explain.
A. Do you favor the proposal to increase spending on technology in our schools?
B. Wearing a seat belt can save a person’s life. Should school buses have seat belts?”
C. A dentist asks his patients, “Do you floss every day?”
Solutions:
A. This question may be biased because it assumes that the respondent is familiar with the proposal. The
responders from people who are unfamiliar with the proposal may not accurately reflect their opinions.
B. This question may be biased because a response of “no” implies that the respondent does not care about the
safety of students riding school buses. Some respondents may feel pressured to give a response of “yes”.
C. This question may be biased because a dentist is asking the question. The responses may not accurately
represent the number of patients who floss every day.
3