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

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APPENDIX A Answers to Select Problems 1.1 Data and Their Uses 1. 2. 3. 4. 5. 6. a. Nominal; ice cream names cannot be ordered, in general. b. Interval; temperatures have order and the differences in temperature can be reasonably discussed. For example, to talk about a difference is meaningful. c. Ratio: Absolute 0 exists since there can be no balance at all. Additionally, it makes sense to talk about ratios. For instance, accounts receivable balances can be, say, 20% higher this month as compared to last. d. Ordinal; there is an ordering, though we can‟t talk about the number 1 candidate as being 2 better than the number 3 candidate. This is because the difference of 1 might not necessarily be the same from 1 to 2 as it would be from 2 to 3. Maybe candidate 3 is a far third. a. 2,121 elements in the sample b. Length of time is a quantitative variable, since it is a numerical measure. a. 15,000 elements in the sample b. A proportion is a quantitative variable, since it is a ratio. a. Observational; the number of animals a family have is not being assigned. Instead, families are simply being asked about how many animals they have. b. The study might have considered families with horses. People with horses likely live on the outskirts of a big city, perhaps being exposed to less pollen. Also, maybe more families have pets because their children do not seem to have allergies to them. a. Observational; the researchers are looking at preexisting habits. They are not attempting to alter the habits to determine what effect doing so might have on measures of reading ability and short-term memory. b. No; perhaps those who watch more television also have other habits that lead them to scoring poorly on such assessments. a. Observational; the opinions of the doctors are not being altered in any way. b. There is a nonresponse bias since not all participants responded. Thus, it might be the case that those with the strongest opinions decided to come forward, whereas the other 17,000 who didn‟t respond might have influenced the poll in a different way. Statistics for Decision-Making in Business © Milos Podmanik Page 220
1.2 Descriptive VS. Inferential Statistics 1. 2. 3. a. $4 million/day b. If all days had the same gross revenue, $4 million would be earned. c. $7.6 d. The amount of gross revenue earned on a given day varies by as much as $7.6 million as another day. e. The film has generated an average of $4 million/day. There is much instability in this average in that the actual gross revenue has varied from $1.6 million to $9.2 million, a range of $7.6 million. It is dangerous to place too many bets on what might happen next, due to the extreme variability in revenues. a. 18 randomly selected college students b. All college students c. Answers vary; spending on clothing, style preference, etc. d. Inferential; they wish to make conclusions about the population of all college students a. 250 packages of cheese selected b. All packages of cheese produced by the company c. 248 or more must pass 4. Consider the following two datasets with a range of 30: 0, 1, 2, 2, 3, 2, 28, 29, 30 0, 1, 2, 3, 4, 3, 4, 2, 1 30 While both have a range of 30, the first dataset has most of its data towards the outer ends of the dataset. In the second dataset, there appears to tightly spaced data, followed by one outlier of 30. The second dataset is, overall, less spread out. 5. The researchers are trying to use CGCC students as a representative population of all college students. This presents a bias, in that CGCC probably does not accurately represent all college students. 2.4 Descriptive Statistics – Variability 1. a. Standard deviation = 5.9; on average, beers in this sample are within 5.9 calories of the average calorie content. Statistics for Decision-Making in Business © Milos Podmanik Page 221
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Statistics for Decision- Making in
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A Note to Students This book is far
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6.3 Confidence Interval for ̂ 202
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which has undergone no additional r
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of transporting such an animal. Not
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Although far from last, we will con
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Account Type Revenue ($) 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
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: 9. Based on the “Structure of a H
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
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