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Unformatted text preview: not welcome. commercial purposes. Note-takers for A+ Notes are Notes in this class are not to be used for Krueger. A Minitab Guide to Statistics, by Meyer and Bundle : includes Minitab statistics software and Text: Statistics (8th Ed), by McClave and Sincich. Office Hours: Tuesday 9:00 AM – 12:00 noon 392-1941 Ext. 227 222 Griffin-Floyd Hall Dennis Wackerly Lecturer: get dirty and the pig likes it. Thought for the day: Never wrestle with a pig. You both STA 2023 Spring 2001 1 http://web.stat.ufl.edu/ dwack/ Course Web page STA 2023 c B.Presnell & D.Wackerly - Lecture 1 STA 2023 c B.Presnell & D.Wackerly - Lecture 1 ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ Sample quizzes, exams Course notes (Friday for following week) How to convert McClave data set to Minitab format How to get started with Minitab “Answers” to projects (2 days before quiz/exam) Projects Formula Sheet FULL version of syllabus (download immediately) ¢ 2 ¡ ¡ ¡ DON’T FALL BEHIND! ACTIVELY do the assignments. Read and use the text. REGULARLY attend both lectures and discussions. HOW TO SUCCEED For Wednesday: Pages 43–46, 50–54. 2.35–2.36 (means only) Exercises : 1.13, 1.19 – 1.23, 2.32 (mean only), For Tomorrow: Pages 2–10, 39 – 42. ¡ 3 INFERENTIAL STATISTICS (p. 3) 2. How can data be used to REACH CONCLUSIONS? – Numerical Summaries – Pie Charts, Stem and Leaf Diagrams – Histograms (Section 2.2) – Summarize Data DESCRIPTIVE STATISTICS (p. 2) 1. How can I COMMUNICATE data to others? with collecting and interpreting data. STATISTICS : a branch of science that is concerned Populations, Samples, Statistical Inference Chapter 1 STA 2023 c B.Presnell & D.Wackerly - Lecture 1 STA 2023 c B.Presnell & D.Wackerly - Lecture 1 ¡ ¡ 4 – Number of semesters to graduate. – Have job or not? – GPA – Income of parents Characteristics (Variables) of interest . students who graduated December 16, 2000. EXAMPLE : Population of interest : the group of U.F. analyse. Contains the information that we actually population. (Defn 1.6, p.5) Sample: A subset of items selected from the unit that is of interest. (Defn 1.5, p.4) Variable: a characteristic of an individual population p.4) of the of the female viewers liked the of the male among female viewers ? commericals. Is the campaign more popular and – The survey also indicated that who like the commercials. (Advertiser cares!!) – Estimate the proportion of ALL viewers in U.S. Inferences of possible interest: TV viewers actually interviewed in the survey. Sample Like commericals or not? Characteristic (Variable) of interest the U.S. ALL TV viewers who have seen the commercials in Population of interest alligator” skin lotion commercials liked them a lot. TV viewers who had seen the Lubriderm “See you later published in USA Today , August 18, 1997, ¡ ¡ ¡ ¡ the items of interest to the data collector. (Defn 1.4, ¡ EXAMPLE : According to a survey of 1,002 adults STA 2023 c B.Presnell & D.Wackerly - Lecture 1 Population: a large body of units representing ALL of 5 ¡ ¡ ¡ STA 2023 c B.Presnell & D.Wackerly - Lecture 1 £ ¢ ¡ 6 the medication. decrease in BP for hypertensive adults who take – Possible Inference : estimate the average – Sample : The 30 individuals used in the study. – Population : ALL hypertensive Adults. adults. adults that are representative of all hypertensive One way : administer the drug to 30 hypertensive HOW? hypertensive adults. new medication in lowering blood pressure in EXAMPLE : We wish to assess the effectiveness of a STA 2023 c B.Presnell & D.Wackerly - Lecture 1 ¡ ¡ 7 Sample Population In f e er population. information contained in a sample taken from that inference about an entire population based on Summary : The objective of statistics is to make an about the population. data to make inferences involves using the sample Each type of inference about the population. decision making , including testing hypotheses prediction of a future observation; nc estimation of some characteristic of the population; forms (p.6): Statistical inference usually takes one of the following STA 2023 c B.Presnell & D.Wackerly - Lecture 1 ¡ ¡ ¡ e 8 ¡ ¡ ¡ of HS seniors took the test, of all high school seniors took populations are actually very different). in the Sun reasonable? (Probably not - the Is the comparison of the average SAT scores given most bound for top Northeastern schools. – In Iowa, only the test. – In Florida Actually students in each of the two states. Presumably, the groups of all college bound What are the populations of interest? Iowa : 1103 ¡ is a reasonable estimate of the or ? 10 mistake? How likely? who like the commericals. Is it likely that we made a in the percentages of male and female TV viewers Example: Suppose we decide that there is a difference close? Within estimate? Is it “close” to the real percentage? How later alligator” commericals, but how good is the proportion of all TV viewers who like the “See you Example: inference. 5. Measure of the goodness or reliability of the 4. The inference about the population. 3. A sample of population units. investigated 2. Identification of one or more Variables to be Florida : 882 ¡ 1. Clear specification of the population of interest. ¡ students from Florida and Iowa were as follows: 5 Elements of a Statistical Inference.(p. 8) 19, 1993), the average total SAT scores in 1993 for ¡ STA 2023 c B.Presnell & D.Wackerly - Lecture 1 ¡ EXAMPLE : According to the Gainesville Sun (August 9 STA 2023 c B.Presnell & D.Wackerly - Lecture 1 ¡ ¡ ¡ add up the squares of the : square the sum of the add up (Sum) all values of : : the first, second, etc. measurements : values values a variable to be measured : Some Notation, Section 2.3 population or sample) to compute meaningful numbers – typically make use of the observed values (in the Numerical Methods – for data summary and inference Section 2.2   " ¢   ¢ £ ¡ through graphical methods (histograms) : Thursday, ¡ Graphical Methods – summarize quantitative data month. © ¢ !   '  # religious affiliation, species of fish). ¥ ¥ ¥ £ freshmen was asked how many movies (s)he saw last ¦ £ ¦ ¦ £ ¢    & & & & £ £    ' '   numerical interpretation (therapy works/does not, ¡ $   £ ¡ ¡ "£ 12 ¡ EXAMPLE : Each individual in a random sample of 5 £ Qualitative Data (p. 8)–classified into groups–no scale (height, weight, temperature, admission rate). STA 2023 c B.Presnell & D.Wackerly - Lecture 1 ¢ ' £ %   ¡ Quantitative Data (p. 8)–measured on a numeric ¢¤ ¥ ¥ ¢ © £ ¥ ¤ ¦ ¤ ¦ £ ¦ £ 11 ¢ ' '  '(    ' ') £ '" ' '" £ & & & ¢ © ¡ £ ( Types of Data § § ¨ ( ( STA 2023 c B.Presnell & D.Wackerly - Lecture 1 ¢ ¥ ¦ if the ’s represent a SAMPLE (p.42) The mean is denoted : & ¦ ¥ ¡ EXAMPLE : For our sample of & students, if the ’s represent a Population (p.42) ¡ values. is the number of ¡ where ¡ (p. 41) set.(p. 41) & ¢ § measurements divided by the number of terms in the values is the sum of the ( ¤ – Population Mean : – Sample Mean : , “mu”(p. 42) (p. 42) – Where is the “middle”? Measure of Central Tendency (p. 40) “Goodness” of a Statistical Inference (p. 8) Five Elements of a Statistical Inference (p. 8) Variables and Samples (p. 4, 5) Population (p. 4) LAST TIME : For Wednesday : Read pages 64 – 66, 56 – 60 Monday : HOLIDAY! 2.43, 2.45, 2.46, 2.49, 2.50, 2.56 For tomorrow: Exercises 2.32, 2.35, 2.36, 2.37, Assignments nice contrast to the real world. Thought for the day: Someone who thinks logically is a STA 2023 c B.Presnell & D.Wackerly - Lecture 2 The Mean of a set of , § Where is the “middle”? ( ¡ ¡ ¡ ¡ ¡ Measures of Central Tendency 13 ¡ STA 2023 c B.Presnell & D.Wackerly - Lecture 1 ¢ 14 ¡ & £ ¢ ¢ £ ¡ Ex. middle two after ordering: § ¡ ¢ median £ £ ¡ ¢ ¢ £ Florida ($1337) Tuition & Fees ($) ¢ ¢ 3000 ¢ ¢ 1000 § median ¡ With an even number of observations, average the Ex. £ observations are arranged in increasing order: ¢ £ & at Public 4yr Institutions The median (p.43) is the “middle value” after the £ Avg Tuition and Fees The Median ¡ D.C. ¢ public 4 year colleges for each state and Washington Where is the Middle? associated with the average yearly tuition and fees at ¡ ¡ £ Proportion of States Another Measure of Central Tendency: £ 0.2 STA 2023 c B.Presnell & D.Wackerly - Lecture 2 ¢ ¢ Given below is the relative frequency histogram. 15 STA 2023 c B.Presnell & D.Wackerly - Lecture 2 ¢ ¢ & 0.0 ¢ ¢ ¡ ¤ ¢ ¢ 16 ¡ £ & ¢ ¢ £ £ £ ) £ & ¡ & ¡ ¢ ' § ¡ £ ¢ ¢ ¡ ¥ ¢ £ ' ¢ £ ¡ ¡ ¢ ¦ © & ¢ ¢¡ ¢ £ ¢ 17 a skewed population, e.g., family incomes. 18 When : one of the twelve numbers. wheel of fortune. The wheel looks like below. You bet on Ex. You are at your favorite casino, about to play the mode Ex. In the last data set the mode is: often in the data set. The mode (p.44) is the measurement that occurs most The Mode STA 2023 c B.Presnell & D.Wackerly - Lecture 2 ¡ representative than the mean of the “typical” member of  ' ' ¢ Because of this, the median is often more ¢ median ¢ while the median in this case is unchanged: ¢ , then the mean becomes ¡ changed to ¢¡ Ex. In the first example, if the largest value, , is median is not. Note: The mean is sensitive to extreme values; the & £ STA 2023 c B.Presnell & D.Wackerly - Lecture 2 ) & 4.8 “C” 3.0 2.6 2.5 4.5 MEDIAN height? our MEAN height, or lull them by reporting our Should we scare the other team by reporting Who should get the ball? 3.2 “B” ¢ Data Set 1: Data Set 2: ¡ median median See Figure 2.17, p. 52. For Data Set 2: range For Data Set 1: range RANGE: largest observation minus smallest (p. 51). One measure of variability is the “spread out” than Data Set 1. Means and medians same, but Data Set 2 more 3.0 4.7 2.5 ) “A” ) Consider two data sets: ¡ Mode Median & & ¢ ¢ Mean ¢ Running Back " (Spread, Dispersion) TIMEOUT! – Call the Statistician. " Measures of Variability : Section 2.5 & & ) § § ( ball is on the 4 yardline, our team is losing by 5 points. & & EXAMPLE : There are 2 seconds left in a football game, STA 2023 c B.Presnell & D.Wackerly - Lecture 2 ¢ 19 " " STA 2023 c B.Presnell & D.Wackerly - Lecture 2 ¢ ¢ ¢ ¢ ¢ ¢ & & ¡ ¡ " " 20 1 ¢ ¢ £ range ¢ 10 " 10 ¢ " " " ¡ " , and 19 19 , but data set II is more spread out than I. , median ¡ ) For both I and II, II. Data Set II. " ¢ ¢ " ¢ ¢ ¢ 1 I. ¢ ¢ ) ¢ & ¡ 22 1 2 3 5 6 7 8 ) is a MORE VARIABILITY. x = 4.0 4 (or is the number of observations in the Population. Where by For a population, we define the population variance LARGER DISTANCES 0 deviation from the mean. observation from the mean. Better to think of variability in terms of distances of each Note that ¢ ¢ & ¡ Consider the data set : & £ ¥  ¢ £ The Variance © Data Set I. ¢ ¦ values. Consider two more data sets: ¢ STA 2023 c B.Presnell & D.Wackerly - Lecture 2 § since it depends only on the largest and smallest " & ¢ & ) ¤ ¡ The range is not a very sensitive measure of variability, 21 ¢ ¢ ) ( ¤ ¢ § § STA 2023 c B.Presnell & D.Wackerly - Lecture 2 ¢ £ ¡ £ ¢ ¢ ¢ ¡ ¡ ¦ § § © ¥ & if we divide by . to get a better ¡ ¡ £ £ £ £ ¡ ¡ ¡ ¡ Note that the Variance is always ¡ £ © Get an UNDERESTIMATE for . when computing & ¡ estimate for § £ £ £ ¡ Divide by ¥ £ ¡ Sum The sample variance (pg. 52) is defined as WHY?? ( £ ¡ © population. " & between the individual values and their mean in the § § ' ¥ £ " § is just the average squared difference Note that for our data set : 2, 3, 7, 5, 3 Note that STA 2023 c B.Presnell & D.Wackerly - Lecture 2 ¡ ' £ ¡ "  ¢ & & &' § § &' 23 ¡ § £ § STA 2023 c B.Presnell & D.Wackerly - Lecture 2 ( ) ( & &  ¡  ( § & ( " ¤ & 24 ¡ ¡ § ¡  © ¥ © ALWAYS giving a sum of .  are positive, variance in “square dollars”. The SAMPLE standard deviation is given by: the variance. The standard deviation is the positive square root of e.g., x’s in dollars square of the original units of measurement, (pg. 52:) The variance is measured in terms of the and the POPULATION standard deviation is larger (smaller) amount of is large (small). is large (small). standard deviation is in dollars). large (small) variation. or large (small) large (small) ( x’s in dollars measurements Quantifies variability using same scale as original The standard deviation cannot be negative. Note that STA 2023 c B.Presnell & D.Wackerly - Lecture 2 The Standard Deviation ¡ " ¡ & Some are negative, ¡ ¡ " &' &' Some of the differences ¡ ¡ Note that 25 § £ £ ¡ £ ¡ ¡ ¡ ¡ £ £ STA 2023 c B.Presnell & D.Wackerly - Lecture 2 26 ...
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This note was uploaded on 12/15/2011 for the course STA 2023 taught by Professor Ripol during the Spring '08 term at University of Florida.

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