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5. The Highway Loss Data Institute publishes data on repair costs resulting from a 5-mph crash test of a car moving forward into a flat barrier. The following table gives data for 10 midsize luxury cars tested in October 2002: Model Repair Cost Audi A6 0 BMW 328i 0 Cadillac Catera 900 Jaguar X 1254 Lexus ES300 234 Lexus IS300 979 Mercedes C320 707 Saab 9-5 670 Volvo S60 769 Volvo S80 4194 a. Using Analysis ToolPak in Excel, generate all descriptive statistics. Discuss the best measure of center and the best measure of spread based on what you see. Justify why these measure were selected. b. Find the -score for the observation 4194. Explain what your answer means in real-world terms. c. Is $4,194 considered an extreme outlier Also use Chebyshev‟s Theorem to numerically reinforce your answer. 6. Cost-to-charge ratios were reported for the 10 hospitals in California with the lowest ratios (San Luis Obispo Tribune, December 15, 2002). The 10 cost-to-charge values were 8.81 10.26 10.2 12.66 12.86 12.96 13.04 13.14 14.7 14.84 Discuss relevant descriptive statistics and a relative frequency distribution . Use your information to make a conclusion about the state of hospitals in California. 7. The technical report “Ozone Season Emissions by State” (U.S. Environmental Protection Agency, 2002) gave the following nitrous oxide emissions (in thousands of tons) for 16 states in the continental United States: 76 22 40 7 30 5 6 136 72 33 0 89 136 39 92 40 13 27 1 63 Generate a brief report about the distribution of nitrous oxide emissions in the sampled states. Use descriptive measures and visuals to justify your answer. Statistics for Decision-Making in Business © Milos Podmanik Page 80
Chapter 3 Probability and Decision Theory When you stop, I mean really stop, and think about how often you think in terms of probabilities, I am confident you‟ll find you use it more often than not. Do you ever decide to get to work by taking one route as opposed to another Would you find yourself making health decisions based on your doctor‟s advice instead of the advice you might receive from a ten-year-old child Have you ever purchased a birthday gift for someone after deep contemplation of what that person might like Do you trust one news network over another What are your decisions based on in these situations Whether or not you‟re willing to give in to your inner nerd, you should admit that you think in terms of chances and likelihood. I imagine that you do have a preferred route. I think that you do trust an expert‟s medical opinion. I believe that you do make a gift purchase after considering what you think the recipient enjoys. I should think there are some networks that you trust more than others. In this chapter, we‟ll explore the nature of probabilistic thinking. You‟ll also notice the phrase “Decision Theory” in the title. Instead of focusing on the trite probability questions involving situations that we don‟t ever encounter, we‟ll concern ourselves with real-world situations where probabilistic reasoning will help us make a decision. Statistics for Decision-Making in Business © Milos Podmanik Page 81
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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.
Page 29 and 30: Chapter 2 Visual Representations of
Page 31 and 32: We now have to enter a formula for
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Page 35 and 36: Alternatively, it is possible to in
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Page 39 and 40: Selected the copied graph. In Chart
Page 41 and 42: 2. The following data represents pe
Page 43 and 44: Frequency 2.2 Visualizing Quantitat
Page 45 and 46: You can either choose to have Excel
Page 47 and 48: If we had additional variables, the
Page 49 and 50: Select PivotChart and select the fi
Page 51 and 52: Frequency To make solid black lines
Page 53 and 54: Relative Frequency Histogram of Cal
Page 55 and 56: a. Using Excel, find the mean and r
Page 57 and 58: ̅ ̅ 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
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Page 83 and 84: Proportion of Rainy Days 1.2 Propor
Page 85 and 86: This means that if samples of HFCS
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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 and 110: ) : The Arizona Cardinals make it t
Page 111 and 112: We could just as well have written,
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
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Object 4 Object 5 Also notice that
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e. 2. Your classmate was absent whe
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3.6 Expected Value Imagine that you
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An expected value is actually not s
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Where The expected value is: , - (
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SOLUTION: We first note that there
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Probability 0.7 0.6 0.5 0.4 0.3 0.2
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Statistics for Decision-Making in B
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For men, we see that the most frequ
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So, we had 10 trials and wanted to
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Example 1: A fair-two sided coin is
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( ) ( ) ( ) ( ) Example 2: A fair,
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Expected Value of a Binomial Random
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f. What is the probability that g.
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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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