unit i - the nature of probability and statistics

8/8/2019 Unit I - The Nature of Probability and Statistics

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y Based on the 2000 census, 40.5 million householdshave two vehicles. (Source: Census Bureau.)

y The average annual salary for an NFL player for the

year 2001 was $1,100,500. (Source: USA TODAY.)y The average cost of a wedding is nearly $19,000.

(Source: Brides Magazine.)

y Women who eat fish once a week are 29% less likely to

develop heart disease. (Source: Harvard School of Public Health.)



y PROBABILITY refers to the chance of an eventoccurring.

y also refers to the study of randomness and uncertainty



y STATISTICS is the science of conducting studies to:

- collect

- organize

- summarize- analyze

- draw conclusions

y from data



y read and understand the various statistical studies

y one may be called on to conduct research in their field

y one can use their knowledge gained from studyingstatistics to become better consumers and citizens



y V ARIABLE

- a characteristic or attribute that can assume different values

y DATA

- values that the variables can assume

- measurements

- observations



y RANDOM V ARIABLES

- variables whose values are determined by chance

y DATA SET- a collection of data values



- consists of the collection, organization,summarization, and presentation of data

Examples:y Nine out of ten on-the-job fatalities are men. (Source:

USA Weekend).

y Expenditures for the cable industry were $5.66 billion

in 1996. (Source: USA TODAY).



- consists of generalizing from samples to populations,performing estimations and hypothesis tests,determining relationships among variables, andmaking predictions

- from samples and populations

Examples:

y In the year 2010, 148 million Americans will beenrolled in an HMO. (Source: USA TODAY).

y Experts say that mortgage rates may soon hit bottom.(Source: USA TODAY).



y POPULATION

- consists of all subjects that are being studied

- human or otherwise

y SAMPLE

- is a group of subjects selected from a population



yQUALITATI V E V ARIABLES

yQUANTITATI V E V ARIABLES



- are variables that can be placed into distinctcategories, according to some characteristic orattribute

Examples:

y softness of different tissue brands

y calmness of the sea



- are numerical and can be ordered or ranked

- can be classified into two:

y QUANTITATI V E DISCRETE V ARIABLES- assume values that can be counted

y QUANTITATI V E CONTINUOUS V ARIABLES

- can assume all values between any two specific values- obtained by measuring



Examples:

y QUANTITATI V E DISCRETE V ARIABLES

- The number of students who enrolled in USC that are

women.

y QUANTITATI V E CONTINUOUS V ARIABLES

- The average GPA (grade point average) forundergraduate applicants to the College of Engineering.



DATA

QUANTITATI V E

CONTINUOUS

DISCRETE

QUALITATI V E



y Depends on how they are:

- Categorized

- Counted- Measured

y These classifications make use of measurement scales



y NOMINAL LE V EL OF MEASUREMENT

y ORDINAL LE V EL OF MEASUREMENT

y INTER V AL LE V EL OF MEASUREMENT

y RATIO LE V EL OF MEASUREMENT



- classifies data into mutually exclusive (non-overlapping), exhausting categories in which no orderor ranking can be imposed on the data

Examples:

y ZIP code

y gender

y eye color



- classifies data into categories that can be ranked;however, precise differences between the ranks do notexist

Examples:

y ranking of tennis players

y grade (A, B, C, D, E)



- ranks data, and precise differences between units of measure do exist; however there is no meaningful zero

Examples:y SAT score

y IQ



- possesses all the characteristics of intervalmeasurement, and there exists a true zero. In addition,true ratios exist when the same variable is measured

on two different members of the population

Examples:

y Height

y Weighty Time



y can be done in a variety of ways

y Surveys one of the most common methods of collectingdata

- telephone surveys

- mailed questionnaire

- personal interview

y can be collected in other ways:- surveying records

- direct observation



y RANDOM SAMPLING

y SYSTEMATIC SAMPLING

y STRATIFIED SAMPLING

y CLUSTER SAMPLING



- subjects are selected by using chance methods orrandom numbers

Example:

y Nursing supervisors are selected using randomnumbers in order to determine annual salaries.



- subjects are selected by numbering each subject of the population and then selecting every k th subject.

Example:y Every seventh customer entering a shopping mall is

asked to select his or her favorite store.



- subjects are selected by dividing the population intogroups (called strata) according to some characteristic thatis important to study then sampling from each group.

Example:

y Mail carriers of a large city are divided into four groupsaccording to gender (male or female) and according to whether they walk or ride on their routes. Then 10 are

selected from each group and interviewed to determine whether they have been bitten by a dog in the last year.



- subjects are selected by using intact groups (calledclusters) which represent the population

Example:y In a large school district, all teachers from two

buildings are interviewed whether they believe thestudents have less homework to do now than in

previous years.



y OBSER V ATIONAL STUDY

- the researcher merely observes what is happening or what has happened in the past and tries to draw

conclusions based on these observations

y EXPERIMENTAL STUDY

- the researcher manipulates one of the variables and

tries to determine how the manipulation influencesother variables



y INDEPENDENT V ARIABLE

y DEPENDENT V ARIABLE

y CONFOUNDING V ARIABLE



- in an experimental study, is the one that is beingmanipulated by the researcher

- also called the explanatory variable



- in an experimental study. the resultant variable uponthe manipulation of the independent variable

- also called the outcome variable



- in an experimental study, is one that influences thedependent or outcome variable but cannot be

separated from the independent variable

unit i - the nature of probability and statistics

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