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

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The most powerful type of variable is one that contains all of the above properties, but whose ratio between two values is meaningful and whose value of zero means a complete absence of the characteristic. While IQ is of an interval scale, it does not make much sense to say that the person with the 120 IQ is 20% . / smarter than the person with the 100 IQ. Certainly we cannot say that a person with 0 IQ has no intelligence at all (this person is probably not even alive!). Consider, however, the median salary of different types of employees. One employee makes $100,000 and another makes $120,000. We can definitely say that the second person makes 20% more than the first person, and we can also say that a values of $0 would indicate a person makes no money at all (total absence of that variable). This variable is of ratio scale. 1.1.4 How We Obtain Data The first question we have after knowing a bit about data is, how do we get it Existing Data In some instances, this data already exists and is available to the researcher. For instance, one can easily go online and find existing data on the U.S. public. We can view things like the average credit card debt per person by state, pounds of grains produced in the United States since 1950, etc. This data is usually available through a number of websites, such as: U.S. Statistical Abstract (U.S. Census) - http://www.census.gov/compendia/statab/ Federal Reserve Board – http://www.federalreserve.org Office of Management and Budget – http://www.whitehouse.gov/omb Department of Commerce – http://www.doc.gov Bureau of Labor Statistics – http://www.bls.gov FedStats - http://www.fedstats.gov/ There are literally thousands of other repositories for existing data. Sometimes a little bit of research unveils a plethora of results. If a company is doing a study of its clients, it may already have a myriad of existing internal data. Conducting a Study to Obtain Data We hear a lot of things coming from our failing media sources. Data is blindly reported, while the method of data collection is ignored. Why do you think there are so many conflicting conclusions reached One week coffee is linked to cancer, while the next it fights cancer. Which is it Many times, observational studies are conducted. There is no experimenter manipulation in this type of study. For example, a zoologist might study elephant eating patterns in various climates to determine whether climate has an effect on caloric intake (response variable – what is measured). He probably cannot manipulate the climate (predictor variable – serves to predict responses) in which the elephant lives (for many reasons, not the least of which is the difficulty Statistics for Decision-Making in Business © Milos Podmanik Page 8
of transporting such an animal. Not to mention, there are startling ethical concerns with such an action!). He probably cannot dictate how much food is in the environment, either. Certainly, he can get an accurate reading of the elephant‟s food intake by following the animal for several days. At the end of the day, the zoologist is merely observing what happens. His conclusions are limited. An experiment, on the other hand, is a type of study in which the experimenter is able to control and manipulate most, if not all, environmental factors. If the experimenter is studying the effects of caffeine on math test scores, for instance, he would have a control group of, perhaps, students who he gives no coffee to and another, experimental group, to which he gives coffee with 60 mg of caffeine. He then measures each group on test score performance (% of total correct): Suppose the experimental group does poorly compared to the control group. Can we be sure that it was due to the caffeine As long as test conditions were the same in each group, yes. If, however, there was something different between the two groups in addition to the presence/absence of caffeine, then the results are not so clear. What if, for instance, they played music with the control group and none with the control group How do we know better performance in the control group wasn‟t an effect of soothing music calming the nerves It could even have been a combination of no caffeine and music. Punchline: In an experiment, we manipulate one factor and hold all other conditions constant. Most of the time it is desirable to run an experiment. The number one reason for this is that we can usually collect evidence that leads to a cause-and-effect relationship, assuming the experiment is conducted properly. In an observational study it is impossible to do this as there are many confounding variables, or variables that might be related to the explanatory and response variable. Consider this classic example: a researcher counts the number of crimes committed in a city and then the number of churches in that city. She does this for quite a few cities. It is found that there is a positive relationship between the number of crimes committed and the number of churches. That is, as crime increases, so do the number of churches. What gives Do these people just repent more often for their guilty consciences Statistics for Decision-Making in Business © Milos Podmanik Page 9
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: which has undergone no additional r
Page 11 and 12: Although far from last, we will con
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
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,
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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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