Math Tech 4 Unit 1 Notes Day 1.notebook. August 18, 2013

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1 Math Tech 4 - Chapter 1 Introduction to Statistics Key Words for Statistics: Data - Information coming from observations, counts, measurements, or responses. Statistics - The science of collecting, organizing, analyzing, and interpreting data in order to make decisions. (drawing conclusions from data) Familiarity of Stats: Most people are familiar with statistics through radio, tv, newspapers and magazines. The average salary for and NFL player today is 1.9 million (Bloomberg Businessweek) The average cost of a wedding is $28,400 (CNN Money) Where are stats used? a) statisticians keep records of the number of yards a running back gains in a season. b) the number of hits a baseball player gets per season. Can you think of any others? 1

2 Why study Statistics? 1) Students must be able to read and understand the various statistical studies performed in their field. This means having and understanding about: > vocabulary > symbols > concepts > statistical procedures 2) Students might have to conduct research in their fields and be able to: design experiments collect data organize data analyze data summarize data 3) Students can use their knowledge from studying statistics to become better citizens and consumers. In other words, make more intelligent choices based on consumer studies. The purpose of chapter 1 is to introduce the basic concepts of probability and statistics. This includes: the branches of statistics - what are they? data definition - what are data? selection of samples - how are they selected? 2

3 Key Words for Statistics: Data Sets - collections of data values Population - an entire group (all of them, whatever they are) Sample - a subset, or part, of a population Data Value or Datum - each value in a data set There are two types of data sets in statistics: populations and samples. Examples: Identifying Data Sets In a recent survey, 1500 adults in the United States were asked if they thought there was solid evidence of global warming. Eight hundred fifty-five of the adults said yes. a) Identify the population and the sample. b) Describe the sample data set. a) Identify the population and the sample. Population - the responses of all adults in the United States Sample - the responses of the 1500 adults in the United States in the survey b) Describe the sample data set. 855 yes's and 645 no's 3

4 The U.S. Department of Energy conducts weekly surveys of approximately 900 gasoline stations to determine the average price per gallon of regular gasoline. On January 11, 2010, the average price was $2.75 per gallon. a) Identify the population and the sample. b) Describe the sample data set. a) Identify the population and the sample. Population - the prices per gallon of regular gasoline at all gas stations in the U.S. Sample - the prices per gallon of regular gasoline at the 900 gasoline stations surveyed b) Describe the sample data set. the 900 prices Key Words for Statistics: Parameter - a numerical description of a population characteristic Statistic - a numerical description of a sample characteristic Examples - Distinguishing between a Parameter and a Statistic 1) A recent survey of 200 college career centers reported that the average starting salary for petroleum engineering majors is $83,121. 2) The 2182 students who accepted admission offers to Northwestern University in 2009 have an average SAT score of ) In a random check of a sample of retail stores, the Food and Drug Administration found that 34% of the stores were not storing fish at the proper temperature. 4

5 1) A recent survey of 200 college career centers reported that the average starting salary for petroleum engineering majors is $83, statistic 2) The 2182 students who accepted admission offers to Northwestern University in 2009 have an average SAT score of parameter More Examples: In 2009, Major League Baseball teams spent a total of $2,655,395,194 on players' salaries. a) Does this numerical value describe a population or a sample? b) Specify whether the numerical value is a parameter or a statistic. 3) In a random check of a sample of retail stores, the Food and Drug Administration found that 34% of the stores were not storing fish at the proper temperature. - statistic a) Does this numerical value describe a population or a sample? Population b) Specify whether the numerical value is a parameter or a statistic. More Key Words for Statistics: Branches of Statistics Descriptive Statistics - the branch of statistics that involves the collection, organization, summarization, and display of data Inferential Statistics - the branch of statistics that involves using a sample to draw conclusions about a population. A basic tool of inferential statistics is probability Parameter 5

6 Statistics Relationships Descriptive Statistics the statistician tries to describe a situation Example Study: The national consensus conducted by the U.S. gov't every 10 years The results give average age, income, and other characteristics of the U.S. population The census bureau must collect the data, then organize, summarize, and present it Statistics A mathematical Science Inferential Statistics the statistician tries to make inferences from samples to populations Consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining the relationships among variables, and making predictions Why use inferential statistics instead of descriptive statistics? Researchers use samples when it is not possible to use the entire population for a statistical study due to expense, time, size of population, medical concerns, etc. A properly selected sample would possess the same or similar characteristics as the subjects in the population. Examples: Descriptive or Inferential Statistics 1) A large sample of men, aged 48, was studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men, 90% were alive at age 65. 2) In a sample of Wall Street analysts, the percentage who incorrectly forecasted high-tech earnings in a recent year was 44%. 1) A large sample of men, aged 48, was studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men, 90% were alive at age 65. descriptive - For unmarried men, approximately 70% were alive at age 65 and For married men, 90% were alive at age 65. inferential - a possible inference is that being married is associated with longer life for men. 2) In a sample of Wall Street analysts, the percentage who incorrectly forecasted high-tech earnings in a recent year was 44%. descriptive - the percentage who incorrectly forecasted high-tech earnings in a recent year was 44%. inferential - the stock market is difficult to forecast, even for professionals. 6

7 More Examples: A survey conducted among 1017 men and women by Opinion Research Corporation International found that 76% of women and 60% of men had a physical examination within the previous year. a) Identify the descriptive aspect of the survey. b) What inferences could be drawn from this survey? a) Identify the descriptive aspect of the survey. 76% of women and 60% of men had a physical exam b) What inferences could be drawn from this survey? a higher percentage of women had an exam the previous year, or will have an exam this year Back to Data: Data - Information coming from observations, counts, measurements, or responses. There are two types of data: Qualitative and Quantitative Qualitative Data - data that consists of attributes, labels, or numerical entries (words) Quantitative Data - data that consists of numerical measurements or counts (numbers) 7

8 Examples: Classifying Data by Type The suggested retail prices of several Ford vehicles are shown in the table. Which data are qualitative data and which are quantitative? Explain your reasoning. Model Suggested retail price Focus Sedan $15,995 Fusion $19,270 Mustang $20,995 Edge $26,920 Flex $28,495 Escape Hybrid $32,260 Expedition $35,085 F-450 $44,145 Which data are qualitative data and which are quantitative? Explain your reasoning. Qualitative - the names of the vehicles these are nonnumerical entries words Quantitative - the prices of the vehicles these are numerical entries numbers More Examples: The populations of several U.S. cities are shown in the table. a) Identify the two data sets. b) Decide whether each data set consists of numerical or nonnumerical entries. c) Specify the qualitative data and the quantitative data. City Population Baltimore, MD 636,919 Jacksonville, FL 807,815 Memphis, TN 669,651 Pasadena, CA 143,080 San Antonio, TX 1,351,305 Seattle, WA 598,541 a) Identify the two data sets. City and Population b) Decide whether each data set consists of numerical or nonnumerical entries. City - nonnumerical Population - numerical c) Specify the qualitative data and the quantitative data. Qualitative - Cities Quantitative - Populations 8

9 Two types of Qualitative Data: Nominal - organizes data by categories; no particular order or ranking > examples: marital status, zip codes, hair color Ordinal - categories can be ranked or ordered; implies position > examples: excellent, fair, poor A, B, C, D 1st place, 2nd place Examples: Classify Data by Level Two data sets are shown. a) Which data set consists of data at the nominal level? b) Which data set consists of data at the ordinal level? Top Five TV Programs (from 5/4/09 to 5/10/09) 1. American Idol - Wednesday 2. American Idol - Tuesday 3. Dancing with the Stars 4. NCIS 5. The Mentalist Network Affiliates in Pittsburgh, PA WTAE - (ABC) WPXI - (NBC) KDKA - (CBS) WPGH - (FOX) a) Which data set consists of data at the nominal level? The second set of data is nominal as these are just the names of the network affiliates. b) Which data set consists of data at the ordinal level? More Examples: Consider the following data sets. For each data set, decide whether the data are at the nominal level or at the ordinal level. a) The final standings for the Pacific Division of the National Basketball Association. b) A collection of phone numbers. The first set of data is ordinal as the set lists the ranks of the TV programs. 9

10 a) The final standings for the Pacific Division of the National Basketball Association. Ordinal - they are ranked b) A collection of phone numbers. Nominal - just categories Two types of quantitative data: Interval - data can be ordered, and meaningful differences between data entries can be calculated. A zero entry simply represents a position on a scale; the entry is not an inherent zero. Ratio - data are similar to data at the interval level, with the added property that a zero entry is an inherent zero. A ratio of two data values can be formed so that one data value can be meaningfully expressed as a multiple of another. Examples: Classifying Data by Level Two data sets are shown. a) Which data set consists of data at the interval level? b) Which data set consists of data at the ratio level? New York Yankees' World Series Victories (Years) 1923, 1927, 1928, 1932, 1936, 1937, 1938, 1939, 1941, 1943, 1947, 1949, 1950, 1951, 1952, 1953, 1956, 1958, 1961, 1962, 1977, 1978, 1996, 1998, 1999, 2000, American League Home Run Totals (by Team) Baltimore Boston Chicago Cleveland Detroit Kansas City Los Angeles Minnesota a) Which data set consists of data at the interval level? The New York Yankees' World Series Victories because you can find differences between the years, but it does not make sense to say that one year is a multiple of another. b) Which data set consists of data at the ratio level? The Home Run Totals because you can find differences and write ratios. From the data you can see that Texas hit 63 more home runs than Cleveland and that New York hit about 1.5 times as many home runs as Seattle. New York Oakland Seattle Tampa Bay Texan Toronto

11 More Examples: Decide whether the data are at the interval level or at the ratio level. a) The body temperatures (in degrees Fahrenheit) of an athlete during an exercise session. b) The heart rates (in beats per minute) of an athlete during an exercise session. a) The body temperatures (in degrees Fahrenheit) of an athlete during an exercise session. Interval because the data can be ordered an meaningful differences can be calculated, but it does not make sense to write a ratio. b) The heart rates (in beats per minute) of an athlete during an exercise session. Ratio, because the data can be ordered, meaningful differences can be calculated, the data can be written as a ratio, and the data set contains an inherent zero. 11

Chap1: What Is Statistics?

Chap1: What Is Statistics? Jie Zhang, Ph.D. Student Account and Information Systems Department College of Business Administration The University of Texas at El Paso jzhang6@utep.edu Spring, 2014 Jie Zhang,