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

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First off, a researcher must decide who his target population is. That is, is he trying to describe all people in the United States All Asian children between the ages of 2 and 5 All elk in Minnesota The population is the set of all people, creatures, things, etc., that we wish to describe. It is often quite time-consuming and costly to conduct a study based on whole populations. Even presidential polls rarely involve more than a couple hundred participants. Through one of a variety of processes, only a select number of elements of the target population will be selected. This select number is referred to as the sample. The process of selecting a sample from the population that we will consider is simple random sampling (SRS). This process helps to ensure that any differences that we notice among sample elements is entirely due to chance and, importantly, that every element in the target population has an equally likely chance of being in the sample. Simple random sampling can be done by many means. You’ve probably heard of the random process of drawing a name from a box to declare the winner of a raffle. More sophisticated means of this are done by a random number generator on a computer, wherein every element of the population is assigned a whole number. Then, a series of random numbers is drawn by a computer and those elements are selected to be in the sample. We can see in the illustration above that our goal is to then make inferences about the population based on our observations of the sample. Just as you might hear from Gallup: “55% of voters plan on voting for Candidate X,” we try to make generalizations based on the target population. As another example, consider a lighting company that is hoping to manufacture a light bulb with a new type of filament. As with any light bulb, a consumer would want to know how long the light bulb is expected to last. Unfortunately, not every light bulb will last equally long as every other light bulb. This means that an average will have to be taken. To add to this, it is not possible to test every single light bulb to determine how long it will last. So, the company decides to randomly test 200 bulbs that come through the assembly line. They hope to use this sample, since it is random and is assumed to be representative of all light bulbs, to estimate the true average lifespan of a light bulb with this new filament. Here is an overview of their inferential statistics process: Statistics for Decision-Making in Business © Milos Podmanik Page 18
(SOURCE: Essentials of Modern Business Statistics, 4 th Edition, Anderson, et. al.) Though it might seem simple enough to conclude that the average light bulb survives for 76 hours, we have to take into account the variability in the lifetimes. That is to say, we need some way to produce a reasonable interval for the true average, since it is the entire population we are looking to describe. A discussion of this inference process is left for future sections. Homework Problems - 1.2 1. Over its first week in the Box Office (12/14/2012 to 12/20/2012), the movie The Hobbit: An Unexpected Journey grossed the following amounts, in millions of dollars (no particular order): 6.9 9.2 1.6 1.9 1.9 1.6 4.9 (SOURCE: www.the-numbers.com) a. Calculate the mean. b. Explain the real-world meaning of the mean. c. Calculate the range. d. Explain the real-world meaning of the range. e. Provide a brief written report (summary) to the producers of the film on how the film is doing and the stability of gross revenues. 2. A marketing firm conducts a focus group with eighteen randomly selected college students to determine their preference for a variety of clothing lines. a. Describe the sample. b. Describe the population. c. What variables might the marketing firm want to measure Statistics for Decision-Making in Business © Milos Podmanik Page 19
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 and 10: of transporting such an animal. Not
Page 11 and 12: Although far from last, we will con
Page 13 and 14: Account Type Revenue ($) New $5,296
Page 15 and 16: For the present time, we‟ll proce
Page 17: Row Labels Average of Revenue ($) M
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,
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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√ ∑( ̅) √ √ 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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