Statistics for Decision- Making in Business - Maricopa Community ...

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Example 4: Suppose that Company 1 (C1) and Company 2 (C2) are competitors in the clothing business. In fact, they both have locations within Chandler Fashion Center Mall. Given previous business experience, the marketing analyst knows that each company has an 80% chance of agreeing to sell a particular line of clothing; However, if C1 agrees to sell the clothing line, C2 wants to stay competitive and so definitely purchases the clothing line. How is the probability that both will agree affected by this new knowledge SOLUTION: In this situation, the decision of C2 is dependent (conditional) upon the decision of C1. Consider a table in which C2‟s choices will reflect the decision of C1. Company 2 Choices When C1 Agrees Company 1 Choices Y Y Y Y Y Y Y Y N N Y Y Y Y Y Y Y Y Y Y ( ) The difference is that C2‟s decisions are all to agree, provided that C1 has agreed. If C1 does not agree, then we‟re not really sure how C2 will act, but we don‟t really care, since the probability we are in search of is when both companies agree! Here we have: ( ) ( ) ( ) Statistics for Decision-Making in Business © Milos Podmanik Page 110
We could just as well have written, So as to be using the decimal form instead of the tabular fractions. If you look back at the reasoning here, you‟ll notice that we have bolded the word “dependent.” In previous sections, we didn‟t have to worry about dependency, since we assumed that the choices of C1 and C2 were independent, that is, one outcome did not affect the other, and vice versa. How do we know whether events are dependent or independent Often times this is based upon some knowledge of the situation or, perhaps, our intuition. Let‟s set up the important ideas here and then we‟ll look at a few examples of dependence versus independence. Probability of Two Events Occurring Simultaneously Given two events, and , then If and are independent events, then ( ) ( ) ( ) ( ) ( ) ( ) where is a symbol to represent the word “and”. We use this in mathematics often. And if and are dependent events, then Or, as it is often written ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) In either instance, the end result involves multiplication. NOTE: and are generic names and thus can be attached to an event in an arbitrary order. As an interesting note, we can make the following conclusion: Statistics for Decision-Making in Business © Milos Podmanik Page 111
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Statistics for Decision- Making in
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A Note to Students This book is far
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6.3 Confidence Interval for ̂ 202
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which has undergone no additional r
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of transporting such an animal. Not
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Although far from last, we will con
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Account Type Revenue ($) New $5,296
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For the present time, we‟ll proce
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Row Labels Average of Revenue ($) M
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(SOURCE: Essentials of Modern Busin
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1.3Statistics in Excel When conduct
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We can make it a bit more presentab
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For measures such as the range, Exc
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We get: We can do the same for Old.
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Chapter 2 Visual Representations of
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We now have to enter a formula for
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We know from the data that this val
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Alternatively, it is possible to in
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16 14 12 10 8 6 Series1 4 2 0 SD D
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Selected the copied graph. In Chart
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2. The following data represents pe
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Frequency 2.2 Visualizing Quantitat
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You can either choose to have Excel
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If we had additional variables, the
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Select PivotChart and select the fi
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Frequency To make solid black lines
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Relative Frequency Histogram of Cal
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a. Using Excel, find the mean and r
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̅ ̅ account for this discrepancy,
Page 59 and 60: 2.3.2 Percentile Another useful too
Page 61 and 62: 2.3.4 Rank What if, on the other ha
Page 63 and 64: Check the “Analysis ToolPak” an
Page 65 and 66: You‟ll immediately notice that a
Page 67 and 68: ̅ 2.4 Descriptive Statistics - Var
Page 69 and 70: √ ∑( ̅) √ √ This is what w
Page 71 and 72: This gives us a nice measure of how
Page 73 and 74: We can immediately see the mean and
Page 75 and 76: Lastly, a normal curve is the most
Page 77 and 78: Frequency ̅ Histogram of TV's Owne
Page 79 and 80: 58.3 34.6 35.5 45.4 38.6 63.8 53.9
Page 81 and 82: Chapter 3 Probability and Decision
Page 83 and 84: Proportion of Rainy Days 1.2 Propor
Page 85 and 86: This means that if samples of HFCS
Page 87 and 88: Are we confident in accusing a lung
Page 89 and 90: 3.2 Joint Probability In the previo
Page 91 and 92: Company 1 Choices Y Y Y Y Y Y Y Y N
Page 93 and 94: There is less than a 1% chance that
Page 95 and 96: We can now see that the situation i
Page 97 and 98: sequence, one ball is chose at rand
Page 99 and 100: 3.3 Probability of Unions Imagine t
Page 101 and 102: Physical .20 .10 .30 Mental .40 .30
Page 103 and 104: SOLUTION: We first arrange this inf
Page 105 and 106: Homework Problems - 3.3 1. A gaming
Page 107 and 108: 3.4 Conditional Probability In many
Page 109: ) : The Arizona Cardinals make it t
Page 113 and 114: That is, the probability that the c
Page 115 and 116: This can happen in one of two ways:
Page 117 and 118: f. All numerical red cards are remo
Page 119 and 120: 3.5 Combinations and Permutations R
Page 121 and 122: 1 st Bushel 2 nd Bushel U1 U1 U2 U2
Page 123 and 124: Which, in its final state gives: Th
Page 125 and 126: Combination - Order Does NOT Matter
Page 127 and 128: ( ) There is only a .9% chance that
Page 129 and 130: 1. Are repeats/replacements allowed
Page 131 and 132: Object 4 Object 5 Also notice that
Page 133 and 134: e. 2. Your classmate was absent whe
Page 135 and 136: 3.6 Expected Value Imagine that you
Page 137 and 138: An expected value is actually not s
Page 139 and 140: Where The expected value is: , - (
Page 141 and 142: SOLUTION: We first note that there
Page 143 and 144: Probability 0.7 0.6 0.5 0.4 0.3 0.2
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Page 147 and 148: For men, we see that the most frequ
Page 149 and 150: So, we had 10 trials and wanted to
Page 151 and 152: Example 1: A fair-two sided coin is
Page 153 and 154: ( ) ( ) ( ) ( ) Example 2: A fair,
Page 155 and 156: Expected Value of a Binomial Random
Page 157 and 158: f. What is the probability that g.
Page 159 and 160: Probability For instance, we see th
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Density 0.25 Time Speng Waiting in
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Suppose we wish to find ( ), that i
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Density Resulting in a standard dev
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Density Without going into detail h
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a. What is the probability that the
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Statistics for Decision-Making in B
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As you can see, this is a difficult
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We wish to know the area of the sha
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We can easily find that the probabi
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In the second section, we can check
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Chapter 6 Sampling Distributions an
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Thus, the standard deviation would
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1.7 to 1.8 1.8 to 1.9 1.9 to 2 2 to
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2.4 to 2.5 2.5 to 2.6 2.6 to 2.7 2.
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The Central Limit Theorem (CLT) has
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can set this up in our applet by ha
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3) We cannot use this sample to cal
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Thus, we need to find the lower and
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We see that the standard deviation
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√ The lower limit is: √ And the
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following data was collected on the
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{ So, we have a set of twenty 1‟s
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DULY CAUTIONED: The assumptions her
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Homework Problems -6.2 1. In a samp
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Since this is a mathematical questi
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Example 3: Many older homes have el
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Hypothesis Test Conclusion Test Say
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Hypothesis Test Conclusion Since yo
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SOLUTION: d. A generic conclusion s
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9. Based on the “Structure of a H
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1.2 Descriptive VS. Inferential Sta
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Relative Frequency 35% 30% 25% 20%
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Symmetric: 35 30 25 20 15 10 5 0 10
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Repair Cost Mean 971 Standard Error
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el freq Nitrous Oxide (thous. Tons)
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Probability Pizza Size Distribution
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e. ( ) f. ; the average response ti
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2. a. The long-run proportion of al
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e. 20% of all children are expected
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e. The middle 50% score between abo
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5. b. This might indicate that the
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̅ We have that ̅ and √ . So our
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6. This is the probability that we
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