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Determine the probability that a man randomly selected from this group died of causes related to heart disease, provided that neither of his parents suffered from heart disease. (PROBLEM SOURCE: SOA/CAS Exam P Sample Questions, Page 5) (Video Solution) Statistics for Decision-Making in Business © Milos Podmanik Page 88
3.2 Joint Probability In the previous section, we began computing probability using some fairly basic ideas. In calculating probabilities, we made a huge assumption: that the found number represents what will occur in the long-run. For instance, if we conduct a study and find that out of 100 people, 94 respond positively to a new energy drink, can we conclude the drink is effective in providing added energy The answer to this question is humbling: it depends upon how the data was collected. Suppose the participants are all college students who tend to consume a large amount of caffeine as it is. Would it be fair for the advertisement to say, “There is a 94% chance that this energy drink will energize you” Not necessarily, since the result only appeared to be valid in a sample of college students. This means that the population must be specified form which the sample was taken. In this case, the population is the set of all college students and the sample is the 100 students who were selected. Thus, perhaps the advertisement should say, “Are you a college student If so, there is a 94% chance that this energy drink will energize you” That is, provided that this sample was a random sample and not a group of college students hand-picked from the respective population. Okay, so you have a data sample collected from a specific population and your goal is to now talk about probabilities. Example 1: Imagine that you work for a marketing agency and your goal is to determine the effectiveness of two different branding approaches to a new line of clothing. The first approach involves establishing a group of Facebook followers by giving incentives for discounts on clothing by becoming a friend of the company. The company hypothesizes that seeing the company logo under on their Facebook account each week, they will gain a strong familiarity and comfort level with the company‟s product. The second approach involves hiring Hollywood actors to endorse the product at film festivals and celebrity appearances. The company then tracks the degree of success of the branding tactic by measuring the number of retail outlets that agree to stock the product based on the branding used. They find that, of the 6 companies exposed to Tactic 1 (T1), 5 agreed to stock the product. Of the 7 companies exposed to Tactic 2 (T2), 5 agreed to stock the product. Statistics for Decision-Making in Business © Milos Podmanik Page 89
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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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Page 55 and 56: a. Using Excel, find the mean and r
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Page 59 and 60: 2.3.2 Percentile Another useful too
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Page 63 and 64: Check the “Analysis ToolPak” an
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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 93 and 94: There is less than a 1% chance that
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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
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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
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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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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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6. This is the probability that we
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