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

More documents

Recommendations

Info

√ Upper limit: √ Similarly, there is a 95% chance that the population mean age is between 22.6 and 28.5. Compare this to our empirical result above of 22.8 to 28.2. We are, again, very close. Homework Problems –6.2 1. Describe, in your own words, what a bootstrap distribution is and why we would want to use one. Be sure to mention the logical process behind building one, as well as the assumptions we are making when we do so. 2. What is a confidence interval Explain in your own words. 3. The following is a random sample of 10 labor costs associated with farming for civilian consumers (in billions of dollars) since 1970. Labor Costs (bill. $) 229.9 303.7 137.9 58.3 81.5 196.6 36.6 168.4 122.9 347.4 (SOURCE: Data randomly sampled from U.S. Statistical Abstract, Table 847) a. Does the Central Limit Theorem apply for this data Why or why not b. Using a bootstrap distribution, calculate a 95% confidence interval for , the true population average labor cost. c. In a complete sentence, interpret the real-world meaning of this value. d. Using the bootstrap distribution and percentiles, how likely is it that a sample of labor costs has a mean greater than $190,000,000,000 4. In Arizona, primarily the Phoenix Metropolitan area, the issue of red-light cameras used to catch red-light runners and speeders was a prominent one for much of the early 2000‟s. Many studies were carried out over this period of debate to determine whether or not they were effective, and whether or not they used taxpayer money appropriately. Suppose the Statistics for Decision-Making in Business © Milos Podmanik Page 200
following data was collected on the revenue generated by randomly sampled red-lights across the valley. The goal is to have, on average, each camera generate $750 and no less than $640 per day. 883 522 590 779 887 615 690 771 843 509 872 840 536 892 880 588 547 770 687 842 832 840 676 555 884 617 517 586 505 552 a. Can the state be 95% confident that the desired average is possible b. Generate a 99% confidence interval for , the population average daily revenue per camera. Explain in a complete sentence what this means. c. Is the CLT valid in this problem Explain. d. Using the assumption that the distribution of ̅ is normally distributed, calculate a theoretical 95% confidence interval for (you will need to estimate the √ standard deviation of ̅‟s and ̅ to estimate . e. In reality, anytime we estimate parameters, like you did above in part d), we actually shouldn‟t assume a normal distribution. Instead, we should assume what is known as a -distribution, which is symmetrical, though has more variability to account for the uncertainty in our estimates. Watch this brief informative video: http://www.youtube.com/watchv=yV-0ReCXW64 Pull up the following applet: http://www.stat.tamu.edu/~west/applets/tdemo.html. You can type in the percentile corresponding to means you want to consider. stands for “degrees of freedom” and can be calculated by taking the sample size minus 1 ( ). (From the video, we know that, if the sample size is really, really big, then the difference between the normal distribution and t-distribution becomes indistinguishable.) The output of this applet will give you the number of standard deviations your endpoints will be on either side of the mean. For example, you will find that a 99% confidence interval for a sample of size 100 has endpoints that are 2.626 standard deviation from the mean (left and right). Let‟s say your sample mean is ̅ and standard deviation . Then, the confidence interval will be an interval around the sample mean. That is, one standard deviation is √ √ (remember, the standard deviation of means requires that we divide the standard deviation among individual ‟s and divide by the square root of the sample size). So, 2.626 standard deviations would be 2.626(0.5) = 1.313 units away from the mean. The endpoints would be 40 – 1.313 and 40 + 1.313, or 38.687 to 41.313. Formulaically, we found: Statistics for Decision-Making in Business © Milos Podmanik Page 201
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 and 122:
1 st Bushel 2 nd Bushel U1 U1 U2 U2
Page 123 and 124:
Which, in its final state gives: Th
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: √ The lower limit is: √ And 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?