MBA 604 Introduction Probaility and Statistics Lecture Notes

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5 Sample Mean and Variance For Grouped Data Example: (weight loss data) Let k = number of classes. Formulas. Weight Loss Data class boundaries mid-pt. freq. xf x2f x f 1 5.0-9.0- 7 3 21 147 2 9.0-13.0- 11 5 55 605 3 13.0-17.0- 15 7 105 1,575 4 17.0-21.0- 19 6 114 2,166 5 21.0-25.0- 23 3 69 1,587 6 25.0-29.0 27 1 27 729 Totals 25 391 6,809 xf xg = n s 2 2 2 x f − ( xf) /n g = n − 1 where the summation is over the number of classes k. Exercise: Use the grouped data formulas to calculate the sample mean, sample variance and sample standard deviation of the grouped data in the weight loss example. Compare with the raw data results. 6 z-score 1. The sample z-score for a measurement x is z = x − x s 2. The population z-score for a measurement x is 17
z = x − µ σ Example. A set of grades has x =75,s = 6. Suppose your score is 85. What is your relative standing, (i.e. how many standard deviations, s, above (below) the mean your score is)? Answer. x − x z = s standard deviations above average. = 85 − 75 6 =1.66 Review Exercises: Data Analysis Please show all work. No credit for a correct final answer without a valid argument. Use the formula, substitution, answer method whenever possible. Show your work graphically in all relevant questions. 1. (Fluoride Problem) The regulation board of health in a particular state specify that the fluoride level must not exceed 1.5 ppm (parts per million). The 25 measurements below represent the fluoride level for a sample of 25 days. Although fluoride levels are measured more than once per day, these data represent the early morning readings for the 25 days sampled. .75 .86 .84 .85 .97 .94 .89 .84 .83 .89 .88 .78 .77 .76 .82 .71 .92 1.05 .94 .83 .81 .85 .97 .93 .79 (i) Show that x = .8588,s 2 = .0065,s= .0803. (ii) Find the range, R. (iii) Using k = 7 classes, find the width, w, of each class interval. (iv) Locate class boundaries (v) Construct the frequency and relative frequency distributions for the data. 18
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 and 14: II. Measures of Variability Given:
Page 15 and 16: x x 2 90 8100 85 7225 65 4225 75 56
Page 17: (iii) Approximation: s range 4 (iv
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
Page 67 and 68: The width of the CI decreases. The
Page 69 and 70:
Please show all work. No credit for
Page 71 and 72:
Chapter 7 Large-Sample Tests of Hyp
Page 73 and 74:
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 =
Page 99 and 100:
Chapter 10 Simple Linear Regression
Page 101 and 102:
3. The r.v. ɛ has a normal distrib
Page 103 and 104:
Optional material Ad Sales Calculat
Page 105 and 106:
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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