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

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It may not come as a large shock that we're dealing with potentially many confounding variables. The simplest one is population. As a city's population increases, more crime is committed and more churches are needed. This is but one possible explanation. Example 1: An educational researcher finds that there is a strong relationship between the number of hours a student studies and his/her grade point average (GPA) List a few possible confounding variables. SOLUTION: There is no guarantee that studying more causes a higher GPA. There are many factors that might influence a higher GPA: More sleep Less stress (maybe due to lack of job) Less television viewing Better study environment More support from family/friends Issues in Planning a Study There are many. Let's consider the following scenario to help illustrate a few. Scenario: Suppose we want to test whether or not a newly designed Freud circular saw blade runs at a lower temperature, and hence causes less burn marks in the wood, than the old blade at 7200 revolutions per minute (RPM). Can we just run the cuts, take the temperatures, and compare I think you know the answer to this. First off, we face many extraneous factors, or variables that are not of interest in the current study but that are thought to affect the response variables. Examples The person doing the cutting with each blade (same or not). The type of wood being cut (is one pine and the other oak). The type of saw (low-power Craftsman, or professional Jet). In order to avoid having these types of factors affect our measurement, we must control them. We can do this by having the same person do the cutting, having both boards being cut exactly the same, and use the same saw for both tests. Secondly, is it sufficient to cut just one board using each blade Definitely not. We must expect that there will be some variation or variability in the temperatures we measure. That is, if I run the cut with the old saw four times, I may read temperatures of 205 , 202 , 209 and 219 . This difference among the measurements is called variability. Thus, to take into account the variability, we must take several replications, or repeated measurements. Then, we would likely use the mean, or average of the replications. Statistics for Decision-Making in Business © Milos Podmanik Page 10
Although far from last, we will consider here one more important concept. You might not think anything of it at first, but do you suppose that it's a good idea to use just two saw blades for the experiment - one old, one new What if we happened to get a faulty blade out of the batch If we run 4 replications with each blade, we might consider having 4 of the old blades and 4 of the new blades. If you have a total of 8 sheets of wood to be cut, is it okay to cut the first 4 with the old blade and the last 4 with the new blade Surprisingly, the answer is "no." Why not Suppose the sheets were delivered freshly cut, and still moist. Well, moisture is subject to gravity, and so the last four boards might be more moist than the top four. Thus, we must randomize each board to one of the two types of saw blades. In other words, we randomly assign each board to a blade. We will not consider this any further at this point. Homework Problems - 1.1 1. Classify each of the following variables as nominal, ordinal, interval, or ratio scale. Justify your answer. a. Favorite flavor of ice cream b. Temperature ( F) c. Accounts Receivable Balance d. Ranking of Presidential Candidates According to Preference 2. Based on a study of 2121 children between the ages of one and four, researchers at the Medical College of Wisconsin concluded that there was an association between iron deficiency and the length of time that a child is bottle-fed (Milwaukee Journal Sentinal, November 26, 2005). a. How many elements does this dataset contain b. Is the variable categorical or quantitative Explain. 3. The student senate at a university with 15,000 students is interested in the proportion of students who favor a change in the grading system to allow for plus and minus grades (e.g., B+, B, B-, rather than just B). Two hundred students are interviewed to determine their attitude toward this proposed change. a. How many elements does this dataset contain b. Is the variable categorical or quantitative Explain. 4. An article titled “Guard Your Kids Against Allergies: Get Them a Pet” (San Luis Obispo Tribune, August 28, 2002) described a study that led researchers to conclude that “babies raised with two or more animals were about half as likely to have allergies by the time they turned six.” a. Is this study an observational study or an experiment Explain. b. Describe a potential confounding variable that illustrates why it is unreasonable to conclude that being raised with two or more animals is the cause of the observed lower allergy rate. Statistics for Decision-Making in Business © Milos Podmanik Page 11
Page 1 and 2: Statistics for Decision- Making in
Page 3 and 4: A Note to Students This book is far
Page 5 and 6: 6.3 Confidence Interval for ̂ 202
Page 7 and 8: which has undergone no additional r
Page 9: of transporting such an animal. Not
Page 13 and 14: Account Type Revenue ($) New $5,296
Page 15 and 16: For the present time, we‟ll proce
Page 17 and 18: Row Labels Average of Revenue ($) M
Page 19 and 20: (SOURCE: Essentials of Modern Busin
Page 21 and 22: 1.3Statistics in Excel When conduct
Page 23 and 24: We can make it a bit more presentab
Page 25 and 26: For measures such as the range, Exc
Page 27 and 28: 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
Page 33 and 34: We know from the data that this val
Page 35 and 36: Alternatively, it is possible to in
Page 37 and 38: 16 14 12 10 8 6 Series1 4 2 0 SD D
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
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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
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2.3.4 Rank What if, on the other ha
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Check the “Analysis ToolPak” an
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You‟ll immediately notice that a
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̅ 2.4 Descriptive Statistics - Var
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√ ∑( ̅) √ √ This is what w
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This gives us a nice measure of how
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We can immediately see the mean and
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Lastly, a normal curve is the most
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Frequency ̅ Histogram of TV's Owne
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58.3 34.6 35.5 45.4 38.6 63.8 53.9
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Chapter 3 Probability and Decision
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Proportion of Rainy Days 1.2 Propor
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This means that if samples of HFCS
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Are we confident in accusing a lung
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3.2 Joint Probability In the previo
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Company 1 Choices Y Y Y Y Y Y Y Y N
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There is less than a 1% chance that
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We can now see that the situation i
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sequence, one ball is chose at rand
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3.3 Probability of Unions Imagine t
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Physical .20 .10 .30 Mental .40 .30
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SOLUTION: We first arrange this inf
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Homework Problems - 3.3 1. A gaming
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3.4 Conditional Probability In many
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) : The Arizona Cardinals make it t
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We could just as well have written,
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That is, the probability that the c
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This can happen in one of two ways:
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f. All numerical red cards are remo
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3.5 Combinations and Permutations R
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1 st Bushel 2 nd Bushel U1 U1 U2 U2
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Which, in its final state gives: Th
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Combination - Order Does NOT Matter
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( ) There is only a .9% chance that
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1. Are repeats/replacements allowed
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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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