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AP Statistics 2016-2017 Chapter 9: Sampling Distributions 9.1: Sampling Distributions 9.2: Sample Proportions 9.3: Sample Means "The essence of all things is numbers."-- (Pythagoras, ca 550 B.C.) The origin of some mathematical words. Calculus: From the Latin word “calculus”, meaning "small stone." Stones were used in many ancient counting processes. Circumference: From the Latin word “circumferre”, meaning "to carry around." Hypotenuse: From the Greek words “hypo” and “teinein”, meaning "to stretch under." Theorem: From the Greek word “theoros”, meaning "spectacle, to look at." To the ancient Greeks, theorems were statements to be observed as laws. Isosceles: From the Greek words “iso” and “skelos”, meaning "equal legs." Integer: From the Latin word “integer”, meaning "perfect, whole, complete." Tangent: From the Latin word “tangere”, meaning "to touch." Trapezoid: From the Greek word “trapeze”, meaning "table." (Many tables today are trapezoid-shaped.) "The theory of probability is at the bottom only common sense" -- (Pierre-Simon LaPlace, 1749-1827) Assignment # 1 (Introduction & §9.1) Read pp. 487 – 489 p. 489 # 9.1 – 9.4 W:[12-14-16] Assignment # 2 (Introduction & §9.1) Th:[12-15-16] In Class – Do Activity 9A/Young Women’s Heights; Read pp. 489 – 492; Read pp. 494 – 499 pp. 492 – 494 # 9.5 – 9.7; pp. 499 – 502 # 9.8 – 9.11 Assignment # 3 (§9.1) F:[12-16-16] pp. 504 – 510. Take notes on all terminology. pp. 511 – 512 # 9.19 – 9.24 Assignment # 4 (§9.2) M:[12-19-16] pp. 504 – 510. Take notes on all terminology. pp. 511 – 512 # 9.19 – 9.24 Assignment # 5 (§9.3) T:[12-20-16] Read pp. 514 – 518; pp. 520 – 521 Activity 9B/Sampling Pennies; pp. 521 – 524 pp. 518 – 519 # 9.31 – 9.34 pp. 524 – 525 # 9.35 – 9.38 Assignment # 6 (Summary 1) Read p. 502 pp. 502 – 504 # 9.12 – 9.18 W:[12-21-16] Assignment # 7 (Summary 2) Read p. 512 pp. 513 – 514 # 9.25 – 9.30 Th:[12-22-16] Assignment # 8 (Summary 3) Read p. 525 pp. 525 – 526 # 9.39 – 9.42 F:[12-23-16] Assignment # 9 (Summary 4) Reading: Read pp. 526 – 527 pp. 527 – 530 # 9.43 – 9.53 T:[01-03-17] Assignment # 10 (Review) Practice Test W:[01-04-17] Assignment # 11 Chapter 9 Test Th:[01-05-17] Key Words, Skills, Terminology and Concepts Sampling Distribution Parameter Statistic Sample Mean ( x ) Population Mean ( ) Sampling Variability Bias of a Statistic Unbiased Statistic Variability of a Statistic Sample Proportion Rules of Thumb 1 & 2 Normal Approximation of the p̂ Distribution Sampling Distribution Standard Deviation of Mean of p̂ Distribution p̂ Distribution of p̂ Mean of Sample Means Standard Deviation of Sampling Distributions Central Limit Theorem from Normal Populations Sample Mean x x Exponential Distribution Usage of the TI-83 – MATH PRB 6:randNorm (mean, std. dev., n) – Will generate n values which are randomly chosen relative to a normal population distribution of a given mean and std. dev. MATH PRB 7:randBin (n observations, p, x # of repeated trails) – Will generate x trials sums of successes out of n attempts. randInt (1, 6, 100) + randInt (1, 6, 100) + randInt (1, 6, 100): Rolls 3 dice (or, a single die three times)100 times and computes the sum. “Simulating Survivor” Program – p.504 "Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty" -- (Archimedes, ca 287 B.C. - 212 B.C.) Hrotswitha of Gandersheim (935 - 1000): The first British woman mathematician of record, Hrotswitha was a Benedictine nun. She made efforts to educate women in mathematics and science. Hrotswitha's ideas about astronomy predated those of Nicholas Copernicus and Isaac Newton by about 500 years. She developed ideas relating to the concept of gravity and did not hold the popular belief that Earth was the center of the universe. "With the help of God, and with His precious assistance, I say that algebra is a scientific art" -- (Omar Khayyam, 1048-1131) Fibonacci (Leonardo of Pisa, 1170-1250): While he is famous for his sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... Fibonacci also made a major contribution to mathematics by advocating for the acceptance of the decimal system in the western world. Born in Italy, he studied under Islamic teachers during a period of his life when he lived in North Africa. He saw the advantage of the decimal system over the cumbersome systems used in Europe. He wrote many mathematical manuscripts that made use of the decimal system. Interestingly, he signed his works "Blockhead."