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MinitabGuide2

# MinitabGuide2 - MINITAB Guide(Chapters 11 and 13 Standard...

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Unformatted text preview: MINITAB Guide (Chapters 11 and 13) Standard Error for Sample Mean MTB > let k1= sigma/sqrt(n) MTB > print k1 where: sigma is the standard deviation of the population. n is the sample size. k1 equals the standard error. Standard error of the sample mean for n=30 and σ=21.25. MTB > let k1= 21.25/sqrt(30) MTB > print k1 Data Display K1 3.87970 Cumulative Probability for Sample Mean: P ( x x ) For a random sample of size n=30 from a MTB > let k1=sigma/sqrt(n) MTB > cdf x k2; SUBC> norm mu k1. MTB > print k2 where: x is the value of sample mean given in the question. mu and sigma are the population mean and standard deviation. n is the sample size. k2 equals the desired probability. population with μ=85 and σ=21.25, calculate P(x 75). MTB > let k1=21.25/sqrt(30) MTB > cdf 75 k2; SUBC> norm 85 k1. MTB > print k2 Data Display K2 0.00497564 Complementary Cumulative Probability for Sample Mean: P ( x x ) MTB > let k1=sigma/sqrt(n) MTB > cdf x k2; SUBC> norm mu k1. MTB > let k3=1­k2 MTB > print k3 where: x is the value of sample mean given in the question. mu and sigma are the population mean and standard deviation. n is the sample size. k3 equals the desired probability. For a random sample of size n=30 from a population with μ=85 and σ=21.25, calculate P(x 100). MTB > let k1=21.25/sqrt(30) MTB > cdf 100 k2; SUBC> norm 85 k1. MTB > let k3=1­k2 MTB > print k3 Data Display K3 0.000055255 For a random sample of size n=30 from a population with μ=85 and σ=21.25, calculate P (75 x 90). MTB > let k1=sigma/sqrt(n) MTB > let k1=21.25/sqrt(30) MTB > cdf x k2; MTB > cdf 75 k2; SUBC> norm mu k1. SUBC> norm 85 k1. MTB > cdf y k3; MTB > cdf 90 k3; SUBC> norm mu k1. SUBC> norm 85 k1. MTB > let k4=k3­k2 MTB > let k4=k3­k2 MTB > print k4 MTB > print k4 where: x and y are the values of sample mean given in Data Display K4 0.896283 the question. mu and sigma are the population mean and standard deviation. n is the sample size. k4 equals the desired probability. In-between Cumulative Probability for Sample Mean: P ( x x y ) 1 Mean and Standard Deviation for Binomial MTB > let k1=n*p MTB > let k2=sqrt(n*p*(1−p)) MTB > print k1­k2 where: p is the probability of success. n is the number of observations. k1 equals the mean. K2 equals the standard deviation. Mean and standard deviation for a binomial with n=100 and p=0.8. MTB > let k1= 100*0.8 MTB > let k2= sqrt(100*0.8*(1­0.8)) MTB > print k1­k2 Data Display K1 80.0000 K2 4.00000 Binomial probabilities for n=10 and p=0.8 MTB > pdf; SUBC> binom 10 0.8. Probability Density Function Binomial with n = 10 and p = 0.8 x P( X = x ) 0 0.000000 1 0.000004 2 0.000074 3 0.000786 4 0.005505 5 0.026424 6 0.088080 7 0.201327 8 0.301990 9 0.268435 10 0.107374 What is the probability of observing (exactly) 3? 0.000786 Cumulative binomial probabilities for n=10 and p=0.8 (Exact) Binomial Probabilities: P(X = x) MTB > pdf; SUBC> binom n p. where: n is the number of observations. p is the probability of success. Cumulative Binomial Probabilities: P(X ≤ x) MTB > cdf; SUBC> binom n p. where: n is the number of trials. p is the probability of success on a single trial. How to use to calculate probabilities: Cumulative binomial probability: P(X ≤ x) (read right from the chart) Complementary cumulative binomial probability (>): P(X > x) = 1 – P(X ≤ x)) Complementary cumulative binomial probability (≥): P(X ≥ x) = 1 – P(X ≤ x-1)) In-between cumulative binomial probability: P(x ≤ X ≤ y) = P(X ≤ y) – P(X ≤ x-1)) MTB > cdf; SUBC> binom 10 .8. Cumulative Distribution Function Binomial with n = 10 and p = 0.8 x P( X <= x ) 0 0.00000 1 0.00000 2 0.00008 3 0.00086 4 0.00637 5 0.03279 6 0.12087 7 0.32220 8 0.62419 9 0.89263 10 1.00000 What is the probability of: a) less than or equal to 3: 0.00086 b) (exactly) 3: 0.00086 – 0.00008 = 0.00078 c) at most 5: 0.03279 d) more than 4: 1 ­ 0.00637 = 0.99363 e) at least 1: 1 – 0.00000 = 1.00000 f) between 4 and 6 inclusive: 0.12087 – 0.00086 = 0.12001 2 ...
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