SQQS1013 Ch1 A122

INTRODUCTION TO Statistics 1.1 WHAT IS STATISTICS? The word statistics derives from classical Latin roots, status which means state. Statistics has become the universal language of the sciences. As potential users of statistics, we need to master both the “science” and the “art” of using statistical methodology correctly. These method include: Carefully defining the situation Gathering data Accurately summarizing the data Deriving and communicating meaningful conclusions Nowadays statistics is used in almost all fields of human effort such as: Education Agricultural Businesses Health Sport Sports A statistician may keeps records of the number of hits a baseball player gets in a season. Financial Financial advisor uses some statistic information to make reliable predictions in investment. Public Health An administrator would be concerned with the number of residents who contract a new strain of flu virus during a certain year. Others Any Idea?….. 1.2 TWO ASPECTS IN STATISTICS Statistics has Two Aspects: Theoretical / Mathematical Statistics Deals with the development, derivation and proof of statistical theorems, formulas, rules and laws. Applied Statistics Involves the applications of those theorems, formulas, rules and laws to solve real world problems. Applied Statistics can be divided into two main areas, depending on how data are used. The two main areas are: Descriptive statistics Inferential statistics What most people think of when they hear the word statistics Includes the collection, presentation, and description of sample data. Using graphs, charts and tables to show data. Refers to the technique of interpreting the values resulting from the descriptive techniques and making decisions and drawing conclusions about the population Determine which of the following statements is descriptive in nature and which is inferential. Of all U.S kindergarten teachers, 32% say that “knowing the alphabet” is an essential skill. Of the 800 U.S kindergarten teachers polled, 32% say that “knowing the alphabet” is an essential skill. Why do we have to study statistics? To read and understand various statistical studies in related field. To communicate and explain the results of study in related field using our own words. To become better consumers and citizens. 1.3 BASIC TERMS OF STATISTICS Population vs. Sample Population Sample A collection of all individuals about which information is desired. ‘Individuals’ are usually people but could also be schools, cities, pet dogs, agriculture fields, etc. There are two kinds of population: Finite population When the membership of a population can be (or could be) physically listed. e.g. the books in library. Infinite population When the membership is unlimited. e.g. the population of all people who might use aspirin. A subset of the population. Parameter vs. Statistic Parameter Statistic A numerical value summarizing all the data of an entire population. Often a Greek letter is used to symbolize the name of parameter. Average/Mean - µ Standard deviation - s e.g. The “average” age at time of admission for all students who have ever attended our college. A numerical value summarizing the sample data. English alphabet is used to symbolize the name of statistic Average/Mean - s Standard deviation - e.g. The “average” height, found by using the set of 25 heights. Variable A characteristic of interest about each individual element of a population or sample. e.g. : A student’s age at entrance into college, the color of student’s hair. Data value The value of variable associated with one element of a population or sample. This value may be a number, a word, or a symbol. e.g. : Farah entered college at age “23”, her hair is “brown”. Data The set of values collected from the variable from each of the elements that belong to sample. e.g. : The set of 25 heights collected from 25 students. Census : a survey includes every element in the population. Sample survey : a survey includes every element in selected sample only. A statistics student is interested in finding out something about the average ringgit value of cars owned by the faculty members of our university. Each of the seven terms just describe can be identified in this situation. i) Population : the collection of all cars owned by all faculty members at our university. ii) Sample : any subset of that population. For example, the cars owned by members the statistics department. iii) Variable : the “ringgit value” of each individual car.(RM) iv) Data value : one data value is the ringgit value of a particular car. Ali’s car, for example, is value at RM 45 000. v) Data : the set of values that correspond to the sample obtained (45,000; 55,000; 34, 0000 ;…). vi) Parameter : which we are seeking information is the “average” value of all cars in the population. vii) Statistic : will be found is the “average” value of the cars in the sample. 1.3.1 Types of Variables Quantitative (numerical) Variables A variable that quantifies an element of a population. e.g. the “total cost” of textbooks purchased by each student for this semester’s classes. Arithmetic operations such as addition and averaging are meaningful for data that result from a quantitative variable. Can be subdivided into two classifications: discrete variables and continuous variables. Discrete Variables Continuous Variables A quantitative variable that can assume a countable number of values. Can assume any values corresponding to isolated points along a line interval. That is, there is a gap between any two values. e.g. Number of courses for which you are currently registered. A quantitative variable that can assume an uncountable number of values. Can assume any value along a line interval, including every possible value between any two values. e.g. Weight of books and supplies you are carrying as you attend class today. Qualitative (attribute, categorical) variables A variable that describes or categorizes an element of a population. e.g.: A sample of four hair-salon customers was surveyed for their “hair color”, “hometown” and “level of satisfaction”. EXERCISE 1 Of the adult U.S. population, 36% has an allergy. A sample of 1200 randomly selected adults resulted in 33.2% reporting an allergy. Describe the population. What is sample? Describe the variable. Identify the statistics and give its value. Identify the parameter and give its value. The faculty members at Universiti Utara Malaysia were surveyed on the question “How satisfied were you with this semester schedule?” Their responses were to be categorized as “very satisfied,” “somewhat satisfied,” “neither satisfied nor dissatisfied,” “somewhat dissatisfied,” or “very dissatisfied.” Name the variable interest. Identify the type of variable. A study was conducted by Aventis Pharmaceuticals Inc. to measure the adverse side effects of Allegra, a drug used for treatment of seasonal allergies. A sample of 679 allergy sufferers in the United States was given 60 mg of the drug twice a day. The patients were to report whether they experienced relief from their allergies as well as any adverse side effects (viral infection, nausea, drowsiness, etc) What is the population being studied? What is the sample? What are the characteristics of interest about each element in the population? Are the data being collected qualitative or quantitative? Identify each of the following as an example of (1) attribute (qualitative) or (2) numerical (quantitative) variables. The breaking strength of a given type of string The hair color of children auditioning for the musical Annie. The number of stop signs in town of less than 500 people. Whether or not a faucet is defective. The number of questions answered correctly on a standardized test. The length of time required to answer a telephone call at a certain real estate office. 1.3.2 Types of Data Data is the set of values collected from the variable from each of the elements that belong to sample. e.g. the set of 25 heights collected from 25 students. Data can be collected from a survey or an experiment. Any Idea?....... Another technique to collect primary data is observation. List the advantages and disadvantages of this technique. 1.3.2.1 Scale of Measurements Data also can be classified by how they are categorized, counted or measured. This type of classification uses measurement scales with 4 common types of scales: nominal, ordinal, interval and ratio. Nominal Level of Measurement Ordinal Level of Measurement A qualitative variable that characterizes (or describes/names) an element of a population. Arithmetic operations not meaningful for data. Order cannot be assigned to the categories. Example: - Survey responses:- yes, no, undecided, - Gender:- male, female A qualitative variable that incorporates and ordered position, or ranking. Differences between data values either cannot be determined or are meaningless. Example: Level of satisfaction:- “very satisfied”, “satisfied”, “somewhat satisfied”, etc. Course grades:- A, B, C, D, or F Interval Level of Measurement Ratio Level of Measurement Involve a quantitative variable. A scale where distances between data are meaningful. Differences make sense, but ratios do not (e.g., 30°-20°=20°-10°, but 20°/10° is not twice as hot!). No natural zero Example: - Temperature scales are interval data with 25oC warmer than 20oC and a 5oC difference has some physical meaning. Note that 0oC is arbitrary, so that it does not make sense to say that 20oC is twice as hot as 10oC. - The year 0 is arbitrary and it is not sensible to say that the year 2000 is twice as old as the year 1000. A scale in which both intervals between values and ratios of values are meaningful. A real zero point. Example: - Temperature measured in degrees Kelvin is a ratio scale because we know a meaningful zero point (absolute zero). - Physical measurements of height, weight, length are typically ratio variables. It is now meaningful to say that 10m is twice as long as 5m. This is because there is a natural zero. Levels of Measurement Nominal - categories only Ordinal - categories with some order Interval - differences but no natural starting point Ratio - differences and a natural starting point EXERCISE 2 1) Classify each as nominal-level, ordinal-level, interval-level or ratio-level. a. Ratings of newscasts in Malaysia. (poor, fair, good, excellent) b. Temperature of automatic popcorn poppers. c. Marital status of respondents to a survey on saving accounts. d. Age of students enrolled in a marital arts course. e. Salaries of cashiers of C-Mart stores. 2) Data obtained from a nominal scale a. must be alphabetic. b. can be either numeric or nonnumeric. c. must be numeric. d. must rank order the data. 3) The set of measurements collected for a particular element is (are) called a. variables. b. observations. c. samples. d. none of the above answers is correct. 4) The scale of measurement that is simply a label for the purpose of identifying the attribute of an element is the a. ratio scale. b. nominal scale. c. ordinal scale. d. interval scale. 5) Some hotels ask their guests to rate the hotel’s services as excellent, very good, good, and poor. This is an example of the a. ordinal scale. b. ratio scale. c. nominal scale. d. interval scale. 6) The ratio scale of measurement has the properties of a. only the ordinal scale. b. only the nominal scale. c. the rank scale. d. the interval scale. 7) Arithmetic operations are inappropriate for a. the ratio scale. b. the interval scale. c. both the ratio and interval scales. d. the nominal scale. 8) A characteristic of interest for the elements is called a(n) a. sample. b. data set. c. variable. d. none of the above answers is correct. 9) In a questionnaire, respondents are asked to mark their gender as male or female. Gender is an example of a a. qualitative variable. b. quantitative variable. c. qualitative or quantitative variable, depending on how the respondents answered the question. d. none of the above answers is correct. 10) The summaries of data, which may be tabular, graphical, or numerical, are referred to as a. inferential statistics. b. descriptive statistics. c. statistical inference. d. report generation. 11) Statistical inference a. refers to the process of drawing inferences about the sample based on the characteristics of the population. b. is the same as descriptive statistics. c. is the process of drawing inferences about the population based on the information taken from the sample. d. is the same as a census. EXERCISE 3 In each of this statements, tell whether descriptive or inferential statistics have been used. The average life expectancy in New Zealand is 78.49 years. A diet high in fruits and vegetables will lower blood pressure. The total amount of estimated losses from Tsunami flood was RM4.2 billion. Researchers stated that the shape of a person’s ears is related to the person’s aggression In 2013, the number of high school graduates will be 3.2 million students. Classify each variable as discrete or continuous. Ages of people working in a large factory Number of cups of coffee served at a restaurant The amount of a drug injected into a rat. The time it takes a student to walk to school The number of liters of milk sold each day at a grocery store Classify each as nominal-level, ordinal level, interval-level, or ratio level. Rating of movies as U, SX and LP. Number of candy bars sold on a fund drive Classification of automobile as subcompact, compact, standard and luxury. Temperatures of hair dryers. Weights of suitcases on a commercial airline. At Sintok Community College 150 students are randomly selected and asked the distance of their house to campus. From this group a mean of 5.2 km is computed. What is the parameter? What is the statistics? What is the population? What is the sample? Matrix No: _______________________ Group:______ TUTORIAL CHAPTER 1 In the following multiple-choice questions, please circle the correct answer. 1. You asked five of your classmates about their height. On the basis of this information, you stated that the average height of all students in your university or college is 65 inches. This is an example of: descriptive statistics statistical inference parameter population 2. A company has developed a new computer sound card, but the average lifetime is unknown. In order to estimate this average, 200 sound cards are randomly selected from a large production line and tested and the average lifetime is found to be 5 years. The 200 sound cards represent the: parameter statistic sample population 3. A summary measure that is computed from a sample to describe a characteristic of the population is called a parameter statistic population sample 4. A summary measure that is computed from a population is called a parameter statistic population sample 5. When data are collected in a statistical study for only a portion or subset of all elements of interest, we are using a: sample parameter population statistic 6. Which of the following is not the goal of descriptive statistics? Summarizing data Displaying aspects of the collected data Reporting numerical findings Estimating characteristics of the population 7. Which of the following statements is not true? One form of descriptive statistics uses graphical techniques One form of descriptive statistics uses numerical techniques In the language of statistics, population refers to a group of people Statistical inference is used to draw conclusions or inferences about characteristics of populations based on sample data 8. Descriptive statistics deals with methods of: organizing data summarizing data presenting data in a convenient and informative way All of the above 9. A politician who is running for the office of governor of a state with 4 million registered voters commissions a survey. In the survey, 54% of the 5,000 registered voters interviewed say they plan to vote for her. The population of interest is the: 4 million registered voters in the state 5,000 registered voters interviewed 2,700 voters interviewed who plan to vote for her. 2,300 voters interviewed who plan not to vote for her 10. A company has developed a new battery, but the average lifetime is unknown. In order to estimate this average, a sample of 500 batteries is tested and the average lifetime of this sample is found to be 225 hours. The 225 hours is the value of a: parameter statistic sample population 11. The process of using sample statistics to draw conclusions about true population parameters is called inferential statistics the scientific method sampling method descriptive statistics 12. Which of the following is most likely a population as opposed to a sample? Respondents to a magazine survey The first 10 students completing a final exam Every fifth student to arrive at the book store on your campus Registered voters in the State of Michigan 13. Researchers suspect that the average number of credits earned per semester by college students is rising. A researcher at Michigan State University (MSU) wished to estimate the number of credits earned by students during the fall semester of 2003 at MSU. To do so, he randomly selects 500 student transcripts and records the number of credits each student earned in the fall term 2003. He found that the average number of semester credits completed was 14.85 credits per student. The population of interest to the researcher is all MSU students all college students in Michigan all MSU students enrolled in the fall semester of 2003 all college students in Michigan enrolled in the fall semester of 2003 14. The collection and summarization of the graduate degrees and research areas of interest of the faculty in the University of Michigan of a particular academic institution is an example of inferential statistics descriptive statistics a parameter a statistic 15. Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called inferential statistics the scientific method sampling method descriptive statistics 16. The estimation of the population average student expenditure on education based on the sample average expenditure of 1,000 students is an example of inferential statistics descriptive statistics a parameter a statistic 17. A study is under way in a national forest to determine the adult height of pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 50 feet tall. It is estimated that the forest contains 32,000 pine trees. The study involves collecting heights from 500 randomly selected adult pine trees and analyzing the results. The sample in the study is the 500 randomly selected adult pine trees the 32,000 adult pine trees in the forest all the adult pine trees taller than 50 feet all pine trees, of any age in the forest 18. The classification of student major (accounting, economics, management, marketing, other) is an example of a categorical random variable. a discrete random variable a continuous random variable a parameter. 19. Most colleges admit students based on their achievements in a number of different areas. The grade obtained in senior level English course (A, B, C, D, or F) is an example of a ________________, or ________________ variable. 20. For each of the following examples, identify the data type as nominal, ordinal, or interval. The letter grades received by students in a computer science class ________________ The number of students in a statistics course ________________ The starting salaries of newly Ph.D. graduates from a statistics program ________________ The size of fries (small, medium, large) ordered by a sample of Burger King customers. _____________________ The college you are enrolled in (Arts and science, Business, Education, etc.) _________________ QQS1013 Elementary Statistics PAGE 2 Chapter 1: Introduction to Statistics Specific definition: Statistics is a collection of procedures and principles for gathering data and analyzing information to help people make decisions when faced with uncertainty. Example applications of Statistics ASPECTS OF STATISTICS Theoretical/Mathematical Statistics Applied Statistics Deals with the development, derivation and proof of statistical theorems, formulas, rules and laws. Involves the applications of those theorems, formulas, rules and laws to solve real world problems. Inferential Statistics Descriptive Statistics Consist of method for collecting, organizing, displaying and summarizing data Consist of methods that use results obtained from sample to make decisions or conclusions about a population Example 1 Example 2 Types of Data Secondary data Data obtained from published material by governmental, industrial or individual sources Published records from governmental, industrial or individual sources. Historical data. Various resources. Experiment is not required. Advantages: Lower cost. Save time and energy. Disadvantages: Obsolete information. Data accuracy is not confirmed. Primary data Necessary data obtained through survey conducted by researcher Primary Data Collection Techniques Data is collected by researcher and obtained from respondent 1. Face to face interview Two ways communication where researcher(s) asks question directly to respondent(s). Advantages: Precise answer. Appropriate for research that requires huge data collection. Increase the number of answered questions. Disadvantages: Expensive. Interviewer might influence respondent’s responses. Respondent refuse to answer sensitive or personal question. 2. Telephone interview Advantages: Quick. Less costly. Wider respondent coverage. Disadvantages: Limited interview duration. Demonstration cannot be performing. Telephone is not answered. 3. Postal questionnaire A set of questions to obtain related information of conducted study. Questionnaires are posted to every respondent. Advantages: Wider respondent coverage. Respondent have enough time to answer questions. Interviewer influences can be avoided. Lower cost. Disadvantages: One way interaction. Low response rate. 25