Statistical Tests and Data Analysis: • Perform statistical tests and mathematical calculations to analyze and interpret data. • 5.A: Perform mathematical calculations, including a. Mathematical equations in the curriculum. b. Means. c. Rates. d. Ratios. e. Percentages. • 5.C Perform chi-square hypothesis testing. Mean 𝑛 1 𝑥ҧ = ෍ 𝑥𝑖 𝑛 𝑖=1 6 1 𝑥ҧ = ෍ 𝑥𝑖 6 𝑖=1 1 𝑥ҧ = (104 + 82 + 121 + 96 + 108 + 73) 6 1 𝑥ҧ = (584 6 𝑥ҧ = 97.3 𝑥ҧ Standard Deviation 𝑠= 2 𝑥)ҧ σ(𝑥𝑖 − 𝑛−1 𝑠= 𝑠= (104 − 97.3)2 +(82 − 97.3)2 +(121 − 97.3)2 +(96 − 97.3)2 +(108 − 97.3)2 +(73 − 97.3)2 5 σ(𝑥𝑖 − 97.3)2 6−1 (6.7)2 +(−15.3)2 +(23.7)2 +(−1.3)2 +(10.7)2 +(−24.3)2 5 𝑠= 𝑠= 𝑠= 44.89 + 234.09 + 561.69 + 1.69 + 114.49 + 590.49 5 1547.34 5 𝑠 = 309.468 𝑠 = 17.59 Standard Error of Mean 𝑠 𝑆𝐸𝑥ҧ = 𝑛 𝑆𝐸𝑥ҧ = 17.59 6 17.59 𝑆𝐸𝑥ҧ = 2.449 𝑆𝐸𝑥ҧ = 7.18 Chi Square (𝑜 − 𝑒) 2 𝑥 =෍ 𝑒 2 2 (𝑜 − 𝑒) 𝑥2 = ෍ 𝑒 2 2 (92 − 78) (64 − 78) 𝑥2 = + 78 78 2 2 (14) (−14) 𝑥2 = + 78 78 196 196 2 𝑥 = + 78 78 𝑥 2 = 2.51 + 2.51 𝑥 2 = 5.02 = 5.0 Laws of Probability If A and B are mutually exclusive, then: P(A or B) = P(A) + P(B) If A and B are independent, then: P(A and B) = P(A) x P(B) Hardy Weinberg 2 2 𝑝 + 2𝑝𝑞 + 𝑞 = 1 𝑝+𝑞 =1 Hardy Weinberg 2 𝐴𝐴 + 1(𝐴𝑎) 𝑝= 𝑡𝑜𝑡𝑎𝑙 2 𝑎𝑎 + 1(𝐴𝑎) 𝑞= 𝑡𝑜𝑡𝑎𝑙 150 𝑝 = = 0.375 400 200 2𝑝𝑞 = = 0.5 400 50 2 𝑞 = = 0.125 400 2 2 𝐴𝐴 + 1(𝐴𝑎) 𝑝= 𝑡𝑜𝑡𝑎𝑙 2 150 + 1(200) 𝑝= 400 𝑥 2 300 + 200 𝑝= 800 500 𝑝= = 0.625 800 2 𝑎𝑎 + 1(𝐴𝑎) 𝑞= 𝑡𝑜𝑡𝑎𝑙 2 50 + 1(200) 𝑞= 400 𝑥 2 100 + 200 𝑞= 800 300 𝑞= = 0.375 800 Rate 𝑑𝑦 𝑑𝑡 𝑑𝑦 (𝑦2 − 𝑦1 ) = 𝑑𝑡 (𝑥2 − 𝑥1 ) 𝑑𝑦 (5.7 − 3.1) = 𝑑𝑡 (4 − 2) 𝑑𝑦 (2.6) = = 1.3 𝑑𝑡 (2) Population Growth 𝑑𝑁 =𝐵−𝐷 𝑑𝑡 𝑑𝑁 = 40 − 20 𝑑𝑡 𝑑𝑁 = 20 𝑑𝑡 Exponential Growth 𝑑𝑁 = 𝑟𝑚𝑎𝑥 𝑁 𝑑𝑡 𝑑𝑁 = 0.25(500) 𝑑𝑡 𝑑𝑁 = 125 𝑑𝑡 Logistic Growth 𝑑𝑁 𝐾−𝑁 = 𝑟𝑚𝑎𝑥 𝑁 𝑑𝑡 𝐾 𝑑𝑁 650 − 500 = 0.25(500) 𝑑𝑡 650 𝑑𝑁 150 = 125 𝑑𝑡 650 𝑑𝑁 𝑑𝑁 = 125 0.231 = 28.85 = 29 𝑑𝑡 𝑑𝑡 Simpson’s Diversity Index 2 𝑛 1−෍ 𝑁 1− 6 27 2 8 + 27 2 13 + 27 2 1 − 0.222 2 + 0.296 2 + 0.481 1 − 0.369 = 0.631 2 Water Potential Ψ = ΨP + ΨS ψ ψ Ψ = -1.0 MPa + -0.6 MPa Ψ = -1.6 MPa Solute Potential ΨS = -iCRT ° ° ψ ψ ° ° pH 𝑝𝐻 = − log 𝐻 + Surface Area & Volume 2 𝑆𝐴 = 4𝜋𝑟 4 3 𝑉 = 𝜋𝑟 3 Sphere 𝑆𝐴 = 4𝜋22 𝑆𝐴 = 4𝜋4 𝑆𝐴 = 16𝜋 1 4 3 𝑉 = 𝜋2 3 4 𝑉 = 𝜋8 3 32 𝑉= 𝜋 3 𝑆𝐴 16𝜋 16𝜋 3 3 = = 𝑥 = 32 𝑉 1 32𝜋 2 𝜋 3 2 Surface Area & Volume 𝑆𝐴 = 2𝑙ℎ + 2𝑙𝑤 + 2𝑤ℎ 𝑉 = 𝑙𝑤ℎ Rectangular Solid 𝑆𝐴 = 2 2 3 + 2 2 4 + 2(4)(3) 𝑆𝐴 = 12 + 16 + 24 𝑆𝐴 = 52 𝑉 = (2)(4)(3) 𝑉 = 24 𝑆𝐴 52 13 = = = 2.17 𝑉 24 6 Surface Area & Volume 𝑆𝐴 = 2𝜋rh + 2π𝑟 2 𝑉 = 𝜋𝑟 ℎ Cylinder 2 𝑆𝐴 = 2𝜋(2)(3) + 2π22 𝑆𝐴 = 2𝜋6 + 2π4 𝑆𝐴 = 12𝜋 + 8𝜋 = 20𝜋 𝑆𝐴 20𝜋 5 = = 𝑉 12𝜋 3 𝑉 = 𝜋22 3 𝑉 = 𝜋(4)3 𝑉 = 12𝜋 Surface Area & Volume 𝑆𝐴 = 6𝑠 𝑉=𝑠 2 3 Cube 𝑆𝐴 = 6(2)2 𝑆𝐴 = 6(4) 𝑆𝐴 = 24 𝑆𝐴 24 = =3 𝑉 8 𝑉 = (2)3 𝑉=8

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