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

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0.433333333333333 to 0.483333333333333 0.483333333333333 to 0.533333333333333 0.533333333333333 to 0.583333333333333 0.583333333333333 to 0.633333333333333 0.633333333333333 to 0.683333333333333 0.683333333333333 to 0.733333333333334 0.733333333333334 to 0.783333333333334 0.783333333333334 to 0.833333333333334 0.833333333333334 to 0.883333333333334 0.883333333333334 to 0.933333333333334 0.933333333333334 to 0.983333333333334 0.983333333333334> We see that this distribution is approximately normal. No surprise there! 350 300 250 200 150 100 50 0 Sampling Distribution of p-hat We calculate the 2.5- and 97.5-percentiles to get the middle 95% of sample proportions generated in the bootstrap sample: (As %) Results Percentile 1: 97.5 0.833 Percentile 2: 2.5 0.500 Thus, we are 95% confident that the proportion of the population of customers that will shop at your store will between 0.50 and 0.83. This is quite a wide interval! At least you know what to expect with 95% confidence! Statistics for Decision-Making in Business © Milos Podmanik Page 204
DULY CAUTIONED: The assumptions here are the same as for bootstrapping with ̅: a random sample is drawn from the population and is representative of the population. If not, the sample is worthless, in any case. 6.3.2 Confidence Interval for ̂ Using Theoretical Results Without providing the intuition for this method, we will simply state the results for the CLT pertaining to the sampling distribution of ̂: Central Limit Theorem for ̂ The sampling distribution of ̂ (which is really just an average of 0‟s and 1‟s) is approximately normal just as long as (similar idea as for the standard CLT). With ̂ ( ̂) , ̂- , ̂- √ ̂( ̂) NOTE: the standard deviation is often referred to as the margin of error in polls. The results above state that, 1. the average proportion of the sampling distribution is the true population proportion. 2. The standard deviation of proportions of the sampling distribution is the above, complex, calculation. AS LONG AS ̂ and ( ̂) , both of which are true statements. We can now proceed: Here, we get to use the standard normal distribution to calculate the number of standard deviations corresponding to the desired interval. So, we know that: ̂ Statistics for Decision-Making in Business © Milos Podmanik Page 205
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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
Page 153 and 154: ( ) ( ) ( ) ( ) Example 2: A fair,
Page 155 and 156: Expected Value of a Binomial Random
Page 157 and 158: f. What is the probability that g.
Page 159 and 160: Probability For instance, we see th
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Page 163 and 164: Suppose we wish to find ( ), that i
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Page 167 and 168: Density Without going into detail h
Page 169 and 170: a. What is the probability that the
Page 171 and 172: Statistics for Decision-Making in B
Page 173 and 174: As you can see, this is a difficult
Page 175 and 176: We wish to know the area of the sha
Page 177 and 178: We can easily find that the probabi
Page 179 and 180: In the second section, we can check
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
Page 187 and 188: 2.4 to 2.5 2.5 to 2.6 2.6 to 2.7 2.
Page 189 and 190: The Central Limit Theorem (CLT) has
Page 191 and 192: can set this up in our applet by ha
Page 193 and 194: 3) We cannot use this sample to cal
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
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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 and 228: Repair Cost Mean 971 Standard Error
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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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