MBA 604 Introduction Probaility and Statistics Lecture Notes

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s = √ s 2 or s = Example: Same sample as before (x = 80) x x−x (x − x) 2 90 10 100 85 5 25 65 -15 225 75 -5 25 70 -10 100 95 15 225 Totals 480 0 700 Therefore s 2 = x x = n (x − x) 2 n − 1 (x−x) 2 n−1 = 480 6 =80 = 700 5 = 140 s = √ s 2 = √ 140 = 11.83 Shortcut Formula for Calculating s 2 and s Example: Same sample s 2 2 ( x − = x) 2 n n − 1 x2 ( − s = x) 2 n n − 1 (or s = √ s 2 ). 13
x x 2 90 8100 85 7225 65 4225 75 5625 70 4900 95 9025 Totals 480 39,100 Numerical methods(Summary) Data: {x1,x2, ···,xn} (i) Measures of central tendency s 2 = 2 ( x − x) 2 n n − 1 = 39, 100 − (480)2 6 5 = 39, 100 − 38, 400 = 5 700 s = = 140 5 √ s2 = √ 140 = 11.83. xi Sample mean: x = n Sample median: the middle number when the measurements are arranged in ascending order Sample mode: most frequently occurring value (ii) Measures of variability Range: r =max−min Sample Variance: s 2 = (xi−x) 2 n−1 Sample standard deviation: s= √ s2 Exercise: Find all the measures of central tendency and measures of variability for the weight loss example. Graphical Interpretation of the Variance: Finite Populations Let N = population size. Data: {x1,x2, ···,xN} Population mean: µ = Population variance: xi N σ 2 (xi − µ) = 2 N 14
Page 1 and 2: MBA 604 Introduction Probaility and
Page 3 and 4: Contents 1 Data Analysis 5 1 Introd
Page 5 and 6: 10 Simple Linear Regression and Cor
Page 7 and 8: 7. How to interpret polls. How many
Page 9 and 10: Formulas: Note: w = 28.6−5.4 6 w
Page 11 and 12: If n is even, the median is the ave
Page 13: II. Measures of Variability Given:
Page 17 and 18: (iii) Approximation: s range 4 (iv
Page 19 and 20: z = x − µ σ Example. A set of g
Page 21 and 22: (i) Complete all entries in the tab
Page 23 and 24: Chapter 2 Probability Contents. Sam
Page 25 and 26: nA = frequency of the event A nA n
Page 27 and 28: provided P (B) > 0. Similarly, P (B
Page 29 and 30: Thus only 32 percent of those perso
Page 31 and 32: (which is equal to Combinations For
Page 33 and 34: 2. Suppose that S = {1, 2, 3, 4, 5,
Page 35 and 36: (Hint: Start by defining the events
Page 37 and 38: The variable X transforms the probl
Page 39 and 40: 3 Discrete Distributions Binomial.
Page 41 and 42: of D elements of the first kind and
Page 43 and 44: One equation is redundant. Choose t
Page 45 and 46: 4. A random variable X has the foll
Page 47 and 48: 1. List the properties for a binomi
Page 49 and 50: Chapter 4 Continuous Distributions
Page 51 and 52: Z-score: OR (simply) Conversely, X
Page 53 and 54: Exercise. Specialize the above resu
Page 55 and 56: 3. Let Z be a standard normal distr
Page 57 and 58: Chapter 5 Sampling Distributions Co
Page 59 and 60: σ ˆP = S.E.( ˆ pq P )= n (iii)
Page 61 and 62: (ii) Find the probability that the
Page 63 and 64: Single Quantitative Population: µ
Page 65 and 66:
where σ is estimated by s. Note: I
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The width of the CI decreases. The
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Please show all work. No credit for
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Chapter 7 Large-Sample Tests of Hyp
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Conclusion: At 100α% significance
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1. Large sample (np ≥ 5,nq≥ 5)
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Test: Sample 2: n2, x2, ˆp2 = x2 n
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orders were recorded, with a sample
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1. Sampled population is normal 2.
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Sample data: Sample 1: n1, x1,s1 Sa
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SUBC> alternative 1. Note: alternat
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RR: Reject H0 if t>2.776 or t X 2
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Q1: Do the data present sufficient
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Training Group 1 2 3 4 65 75 59 94
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GT: Grand Total. Computational Form
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Treatments t1 t2 t3 Bi s1 17 34 23
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Solution to (ii) Test. H0 : µ1 =
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Chapter 10 Simple Linear Regression
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3. The r.v. ɛ has a normal distrib
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Optional material Ad Sales Calculat
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Estimator mean: µ β1 ˆ = β1 Est
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(ii) The population coefficient of
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The regression equation is y=46.5 +
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Source DF SS MS F P Regression 7626
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4. The random components of any two
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MINITAB. Use REGRESS command to reg
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Q1. What is the prediction equation
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MBA 604 Introduction Probaility and Statistics Lecture Notes

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