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

More documents

Recommendations

Info

1 st Bushel 2 nd Bushel U1 U1 U2 C U2 C This leaves us with three possibilities. So, our probability should be: ( ) Wait! This is the same as our earlier calculation of ( ) Since we get the same answer, one might think that it must not matter which approach we take. Many times, it doesn‟t; however, “many” is not satisfying enough, since this leaves us prone to mistakes under different circumstances. Let‟s analyze the full situation two different ways. We found that if we don‟t eliminate order differences, then we can write the probability as: If we did (correctly) eliminate order differences, notice that we cut the number of possibilities in half, that is, divided by 2. You‟ll notice that 2 is the same thing as . So, let‟s divide out the number of duplicates from top and bottom: And Statistics for Decision-Making in Business © Milos Podmanik Page 122
Which, in its final state gives: This does look rather complicated, but remember that it follows from some fairly simple things that we have built up on. Also notice that both the top fraction and the bottom fraction have . Ah, yes! So that‟s why the order-not-eliminated and order-eliminated answers are the same: ⏟ ⏟ While this works out beautifully in this example, it is not always true, and so we must take care to observe whether order difference is important. We will see examples later where this difference will come into play, but those situation are a bit more advanced. Let‟s simplify this horrid notation a bit. Suppose that there are a total of are to be drawn. items and of those Permutation – Order Does Matter If order is not to be eliminated (in cases where order is important), then the number of ways to select things from the given is called a permutation and is denoted: ( ) NOTE: ( ) , that is, factorial is not distributable!! Subtract first, then use factorial. For our numerator, we had selected 2 uncontaminated bushels from a total of 18 uncontaminated bushels. According to our new notation, this can be written as: ( ) And this is precisely what we have written for the numerator! For our denominator, we had selected 2 (general) bushels from a total of 20 (general) bushels, since we want to know the total number of ways 2 objects can come out of 20. Statistics for Decision-Making in Business © Milos Podmanik Page 123
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 $5,296
Page 15 and 16:
For the present time, we‟ll proce
Page 17 and 18:
Row Labels Average of Revenue ($) 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,
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
Page 69 and 70:
√ ∑( ̅) √ √ This is what w
Page 71 and 72: This gives us a nice measure of how
Page 73 and 74: We can immediately see the mean and
Page 75 and 76: Lastly, a normal curve is the most
Page 77 and 78: Frequency ̅ Histogram of TV's Owne
Page 79 and 80: 58.3 34.6 35.5 45.4 38.6 63.8 53.9
Page 81 and 82: Chapter 3 Probability and Decision
Page 83 and 84: Proportion of Rainy Days 1.2 Propor
Page 85 and 86: This means that if samples of HFCS
Page 87 and 88: Are we confident in accusing a lung
Page 89 and 90: 3.2 Joint Probability In the previo
Page 91 and 92: Company 1 Choices Y Y Y Y Y Y Y Y N
Page 93 and 94: There is less than a 1% chance that
Page 95 and 96: We can now see that the situation i
Page 97 and 98: sequence, one ball is chose at rand
Page 99 and 100: 3.3 Probability of Unions Imagine t
Page 101 and 102: Physical .20 .10 .30 Mental .40 .30
Page 103 and 104: SOLUTION: We first arrange this inf
Page 105 and 106: Homework Problems - 3.3 1. A gaming
Page 107 and 108: 3.4 Conditional Probability In many
Page 109 and 110: ) : The Arizona Cardinals make it t
Page 111 and 112: We could just as well have written,
Page 113 and 114: That is, the probability that the c
Page 115 and 116: This can happen in one of two ways:
Page 117 and 118: f. All numerical red cards are remo
Page 119 and 120: 3.5 Combinations and Permutations R
Page 121: 1 st Bushel 2 nd Bushel U1 U1 U2 U2
Page 125 and 126: Combination - Order Does NOT Matter
Page 127 and 128: ( ) There is only a .9% chance that
Page 129 and 130: 1. Are repeats/replacements allowed
Page 131 and 132: Object 4 Object 5 Also notice that
Page 133 and 134: e. 2. Your classmate was absent whe
Page 135 and 136: 3.6 Expected Value Imagine that you
Page 137 and 138: An expected value is actually not s
Page 139 and 140: Where The expected value is: , - (
Page 141 and 142: SOLUTION: We first note that there
Page 143 and 144: Probability 0.7 0.6 0.5 0.4 0.3 0.2
Page 145 and 146: Statistics for Decision-Making in B
Page 147 and 148: For men, we see that the most frequ
Page 149 and 150: So, we had 10 trials and wanted to
Page 151 and 152: 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
Page 161 and 162: Density 0.25 Time Speng Waiting in
Page 163 and 164: Suppose we wish to find ( ), that i
Page 165 and 166: Density Resulting in a standard dev
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
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
Page 211 and 212:
Example 3: Many older homes have el
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
Page 229 and 230:
el freq Nitrous Oxide (thous. Tons)
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
Page 245 and 246:
6. This is the probability that we
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?