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

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Thus, our interval is: ( ) Or ( ) This is a bit wider, accounting for the extra variability in estimating and . 6.3 Confidence Interval for ̂ 7.1 The Concept Behind Hypothesis Testing 1. The null hypothesis is assumed to be true and is usually based on what has been observed before. The alternative hypothesis is what we would like to test, which is something that would challenge past observations or assumptions about a population. 2. We assume it is true because it is based on past observations or research. For example, if the Census Bureau finds that 35% of Americans enjoy hypothesis testing, then this is typically based on some fairly extensive research. If a researcher believes this rate is greater in his community, then he can test his alternative hypothesis. 3. 4. 5. Statistics for Decision-Making in Business © Milos Podmanik Page 244
6. This is the probability that we reject the null hypothesis when it is, in fact, true. That is ( ) . This allows us to be 95% confident that we fail to reject when it is true, a correct decision. 7. 1) Hypotheses: 8. 2) Decision Rule: We will reject the null hypothesis when the likelihood of observing something as small or smaller than 52 out of 1000 bushels is no larger than a 1% probability, under the assumption of the null hypothesis. That is, ( ) 3) We will reject if the observed value of is smaller than some cutoff value of . 4) Based on the sample evidence, we will either: a. Reject in favor of of insect-related crop destruction for the farmer‟s new method. b. Fail to reject . We do not have sufficient evidence to conclude that the farmer‟s new method is better than his old method. 1) Hypotheses: 2) Decision Rule: We will reject the null hypothesis when the likelihood of observing something as large or larger than ̅ is no larger than a 5% probability, under the assumption of the null hypothesis. That is, ( ̅ ) ̅ 3) We will reject if the observed average of is larger than some cutoff value of ̅. 4) Based on the sample evidence, we will either: a. Reject in favor of out of 5 questions are answered correctly by his students (as of recent observations). b. Fail to reject . We do not have sufficient evidence to conclude that the instructor‟s more recent students do better on the AP exam than his former students. 9. 1) Hypotheses: Statistics for Decision-Making in Business © Milos Podmanik Page 245
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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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We can easily find that the probabi
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In the second section, we can check
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Chapter 6 Sampling Distributions an
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Thus, the standard deviation would
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1.7 to 1.8 1.8 to 1.9 1.9 to 2 2 to
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2.4 to 2.5 2.5 to 2.6 2.6 to 2.7 2.
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The Central Limit Theorem (CLT) has
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can set this up in our applet by ha
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Page 207 and 208: Homework Problems -6.2 1. In a samp
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Page 213 and 214: Hypothesis Test Conclusion Test Say
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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: ̅ We have that ̅ and √ . So our
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