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

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el freq CC Ratios Mean 12.35 Standard Error 0.62 Median 12.91 Mode #N/A Standard Deviation 1.97 Sample Variance 3.90 Kurtosis -0.50 Skewness -0.60 Range 6.03 Minimum 8.81 Maximum 14.84 Sum 123.47 Count 10.00 There do not appear to be extreme outliers, since the mean and median are close. However, based on the mean being smaller than the median, and the skewness value being negative, there is a slight left-skew to the distribution. The standard deviation tells us that average CC ratios are within 0.62, or 62% points, of the mean. We verify these notions by consider the histogram 45.00% 40.00% 35.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% CC Ratio Distribution CC Ratio We should also be careful to note that there is not very much data available, which is why we don‟t distinctly see a skew. 7. Statistics for Decision-Making in Business © Milos Podmanik Page 228
el freq Nitrous Oxide (thous. Tons) Mean 46.35 Standard Error 9.395205 Median 36 Mode 40 Standard Deviation 42.01663 Sample Variance 1765.397 Kurtosis 0.09474 Skewness 0.949789 Range 136 Minimum 0 Maximum 136 Sum 927 Count 20 30% 25% 20% 15% 10% 5% 0% Nitrous Oxide Distribution Nitrous Oxide (thous. Tons) The distribution of nitrous oxide emissions is skewed to the right indicating that most states have relatively low emissions, whereas fewer states have relatively high emissions. We note that the median is a good measure, indicating that 36 thousand tons is the 50 th percentile. There are two outliers of 136 thousand tons. For this value, , indicating that at least around 75% of all values in the data set are within 2.1 standard deviations of the mean. Thus, 136 can be considered a mild outlier. 3.2 Joint Probability Statistics for Decision-Making in Business © Milos Podmanik Page 229
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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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16 14 12 10 8 6 Series1 4 2 0 SD D
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Selected the copied graph. In Chart
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2. The following data represents pe
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Frequency 2.2 Visualizing Quantitat
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You can either choose to have Excel
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If we had additional variables, the
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Select PivotChart and select the fi
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Frequency To make solid black lines
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Relative Frequency Histogram of Cal
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a. Using Excel, find the mean and r
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̅ ̅ 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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Page 181 and 182: Chapter 6 Sampling Distributions an
Page 183 and 184: Thus, the standard deviation would
Page 185 and 186: 1.7 to 1.8 1.8 to 1.9 1.9 to 2 2 to
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Page 189 and 190: The Central Limit Theorem (CLT) has
Page 191 and 192: can set this up in our applet by ha
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Page 195 and 196: Thus, we need to find the lower and
Page 197 and 198: We see that the standard deviation
Page 199 and 200: √ The lower limit is: √ And the
Page 201 and 202: following data was collected on the
Page 203 and 204: { So, we have a set of twenty 1‟s
Page 205 and 206: DULY CAUTIONED: The assumptions her
Page 207 and 208: Homework Problems -6.2 1. In a samp
Page 209 and 210: Since this is a mathematical questi
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Page 213 and 214: Hypothesis Test Conclusion Test Say
Page 215 and 216: Hypothesis Test Conclusion Since yo
Page 217 and 218: SOLUTION: d. A generic conclusion s
Page 219 and 220: 9. Based on the “Structure of a H
Page 221 and 222: 1.2 Descriptive VS. Inferential Sta
Page 223 and 224: Relative Frequency 35% 30% 25% 20%
Page 225 and 226: Symmetric: 35 30 25 20 15 10 5 0 10
Page 227: Repair Cost Mean 971 Standard Error
Page 231 and 232: Probability Pizza Size Distribution
Page 233 and 234: e. ( ) f. ; the average response ti
Page 235 and 236: 2. a. The long-run proportion of al
Page 237 and 238: e. 20% of all children are expected
Page 239 and 240: e. The middle 50% score between abo
Page 241 and 242: 5. b. This might indicate that the
Page 243 and 244: ̅ We have that ̅ and √ . So our
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