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When answering these questions, it is fairly useful to fully organize the data by providing all totals: Smoker/Lung Cancer Yes No Smoker TOTALS Yes 688 650 1,338 No 21 59 80 Lung Cancer TOTALS: 709 709 1,418 1. Since there is a total of 1,418 individuals being considered and, of those, 709 developed lung cancer, ( ) We must be careful in using this probability as it doesn‟t really reveal anything about the link between lung cancer and smoking, since 709 patients with lung cancer and 709 without lung cancer were chosen to participate in the study to begin with. This is a probability that was fixed by the researchers. 2. There is a total of 1,338 individuals in the study that smoke (we are limited to the smokers only, per the way the question is stated). Of those individuals, 688 have lung cancer. ( ) Slightly over half of the patients who are smokers developed lung cancer. This number is frighteningly large. Before we jump the gun in assuming that smoking is the culprit here, we should probably consider what happens with nonsmokers. 3. There is a total of 80 nonsmokers in the group. Of them, 21 developed lung cancer. ( ) Slightly more than one-fourth of non-smokers developed lung cancer. This number appears to be significantly less severe than for the smokers. We speculate (but did not prove) that smoking increases the likelihood that one will develop lung cancer. 4. There are 709 patients with lung cancer. Of these, 688 smoke. ( ) Statistics for Decision-Making in Business © Milos Podmanik Page 86
Are we confident in accusing a lung cancer patient of being a smoker According to this data, perhaps. The moral of the story is: analyze the situation from a variety of lenses. What appears to be true might be an illusion of what we see immediately! Sometimes, however, it is about what the naked eye does not detect. This is what makes good analysts. Homework Problems - 3.1 1. A classmate of yours was absent when this section was discussed. Explain to her what a probability is in your own words. 2. In a study performed by Cambridge University in the United Kingdom, it was found that, “One out of three people is overwhelmed by the latest breakthroughs in technology.” (SOURCE: http://www.gev.com/2011/07/study-one-out-of-three-people-overwhelmedby-technology/). Primarily, individuals are overwhelmed by how much information is available through the use of social networks and smartphones, to name just two. Explain what is meant by this and explain in terms of probabilistic reasoning. 3. In a 2007 survey conducted by DDB Worldwide, an internationally known advertising company, the following question was asked of a random group of 217 participants: “Is consistency in branding becoming any more or less important” The following table displays the results: Response Number of respondents More important 143 Less important 74 Find the probability that a respondent believes that consistency in branding is: a. More important, then explain what this means. b. Less important, then explain what this means. 4. The probability that a visit to a primary care physician‟s (PCP) office results in neither lab work nor referral to a specialist is 35%. Of those coming to a PCP‟s office, 30% are referred to specialists and 40% require lab work. Determine the probability that a visit to a PCP‟s office results in both lab work and referral to a specialist. (Video Solution) 5. A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least one parent who suffered from heart disease, and, of these 312 men, 102 died from causes related to heart disease. Statistics for Decision-Making in Business © Milos Podmanik Page 87
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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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Page 39 and 40: Selected the copied graph. In Chart
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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
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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 81 and 82: Chapter 3 Probability and Decision
Page 83 and 84: Proportion of Rainy Days 1.2 Propor
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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
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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
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Page 135 and 136: 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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