According to Wikipedia point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population means).
Statistical inference: Statistical Power, ANOVA, and Post Hoc testsEugene Yan Ziyou
This deck was used in the IDA facilitation of the John Hopkins' Data Science Specialization course for Statistical Inference. It covers the topics in week 4 (statistical power, ANOVA, and post hoc tests).
The data and R script for the lab session can be found here: https://github.com/eugeneyan/Statistical-Inference
This presentation covers important topics such as
Multiple Independent Random Variables or i.i.d samples.
Expectations or Expected values
T-Distribution
Central Limit Theorem
Asymptotics & Law of Large Numbers
Confidence Intervals
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 11: Goodness-of-Fit and Contingency Tables
11.2: Contingency Tables
According to Wikipedia point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population means).
Statistical inference: Statistical Power, ANOVA, and Post Hoc testsEugene Yan Ziyou
This deck was used in the IDA facilitation of the John Hopkins' Data Science Specialization course for Statistical Inference. It covers the topics in week 4 (statistical power, ANOVA, and post hoc tests).
The data and R script for the lab session can be found here: https://github.com/eugeneyan/Statistical-Inference
This presentation covers important topics such as
Multiple Independent Random Variables or i.i.d samples.
Expectations or Expected values
T-Distribution
Central Limit Theorem
Asymptotics & Law of Large Numbers
Confidence Intervals
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 11: Goodness-of-Fit and Contingency Tables
11.2: Contingency Tables
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Where we explain how the cryptographic ideas are used to create a crypto asset on the block chain. This one part of a three part slide deck. For the full deck and the context please visit http://bit.ly/pm-bbc
Work hard to make certain that the results you have are accurate b.docxkeilenettie
Work hard to make certain that the results you have are accurate based on class material.
Use T- table and Z-table when needed.
Feel free to consult and cite the notes and previous assignments in preparing this exam.
Please show all of your working out so I am able to see your path to your answer. Mistakes will be penalized however showing your working out will allow me to deduct fewer points. If no working out is shown, I will be forced to deduct full points for mistakes.
**
.
Z table and T table are attached.
Please read carefully
!
When appropriate and possible, express your answer in the same units as the variable.
For example, if the question asks for the mean years of formal education and you have calculated the mean to be 18.44, your answer should be expressed as “
18.44 years of formal education
.”
Equations to Use
Median Position = N+1/2
The
Median Value
is the midpoint between the scores.
Mean
=
å
x
/ N
Standard Deviation =
Z score =
x – mean / standard deviation
CI =
For samples sizes ≥ 100,
the formula for the
CI
is:
CI
=
(the sample mean) + & - Z(
s / √N – 1)
CI =
For samples sizes < 100,
the formula for the
CI
is:
CI
=
(the sample mean) + & - T(
s / √N – 1)
Please answer the following questions:
You are interested in the effects of release with aftercare for a small number of drug offenders. The number of additional months without drug use for a sample
of 6 offenders
is recorded. The data on the six (6) subjects are as follows:
2
8
5
2
8
2
What are the
median position
and the
median value
?
(3 points)
What is the mean?
(
2 points)
What is the most frequently occurring score in this distribution of scores - mode?
(2 point)
2. Computation of a mode is most appropriate when a variable is measured at which level?
(2 points)
A. interval-ratio
B. ordinal
C. nominal
D. discrete
Answer: ________________________
3.
Assume that the distribution of a college entrance exam is normal with
a mean of 500 and a standard deviation of 100
.
For each score below, find the equivalent Z score, the percentage of the area above the score, and the percentage of the area below the score.
( 5 each = total 10 points)
Score Z score % Area Above % Area Below
a) 437
b) 526
4. The class intervals below represent ages of respondents. Which list is both exhaustive and mutually exclusive?
(2 points)
A. 119–120, 120–121, 121–122
B. 119–120, 121–122, 123–124
C. 119–121, 123–125, 127–129
D. 119–120, 122–123, 125–126
Answer: ______________________
5. The parole board is alarmed by the low number of years actually spent in prison for those inmates sentences to 15-year sentences. To help them make parole recommendations they gather data on the number of years served for a small sample of 7 (
seven) p
otential parolees. The number of years served for these seven parol.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
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Z-scores: Location of Scores and Standardized Distributions
1. Chapter 5
z-Scores: Location of Scores and
Standardized Distributions
PowerPoint Lecture Slides
Essentials of Statistics for the
Behavioral Sciences
Eighth Edition
by Frederick J. Gravetter and Larry B. Wallnau
2. Chapter 5 Learning Outcomes
• Understand z-score as location in distribution1
• Transform X value into z-score2
• Transform z-score into X value3
• Describe effects of standardizing a distribution4
• Transform scores to standardized distribution5
3. Tools You Will Need
• The mean (Chapter 3)
• The standard deviation (Chapter 4)
• Basic algebra (math review, Appendix A)
4. 5.1 Purpose of z-Scores
• Identify and describe location of every
score in the distribution
• Standardize an entire distribution
• Take different distributions and make them
equivalent and comparable
6. 5.2 z-Scores and Location in a
Distribution
• Exact location is described by z-score
– Sign tells whether score is located above or below
the mean
– Number tells distance between score and mean in
standard deviation units
8. Learning Check
• A z-score of z = +1.00 indicates a position in a
distribution ____
• Above the mean by 1 pointA
• Above the mean by a distance equal to 1
standard deviationB
• Below the mean by 1 pointC
• Below the mean by a distance equal to 1
standard deviationD
9. Learning Check - Answer
• A z-score of z = +1.00 indicates a position in a
distribution ____
• Above the mean by 1 pointA
• Above the mean by a distance equal to 1
standard deviationB
• Below the mean by 1 pointC
• Below the mean by a distance equal to 1
standard deviationD
10. Learning Check
• Decide if each of the following statements
is True or False.
• A negative z-score always indicates
a location below the meanT/F
• A score close to the mean has a
z-score close to 1.00T/F
11. Learning Check - Answer
• Sign indicates that score is below
the meanTrue
• Scores quite close to the mean
have z-scores close to 0.00
False
12. Equation (5.1) for z-Score
X
z
• Numerator is a deviation score
• Denominator expresses deviation in standard
deviation units
13. Determining a Raw Score
From a z-Score
• so
• Algebraically solve for X to reveal that…
• Raw score is simply the population mean plus
(or minus if z is below the mean) z multiplied
by population the standard deviation
X
z zX
15. Learning Check
• For a population with μ = 50 and σ = 10, what
is the X value corresponding to z = 0.4?
•50.4A
•10B
•54C
•10.4D
16. Learning Check - Answer
• For a population with μ = 50 and σ = 10, what
is the X value corresponding to z = 0.4?
•50.4A
•10B
•54C
•10.4D
17. Learning Check
• Decide if each of the following statements
is True or False.
• If μ = 40 and 50 corresponds to
z = +2.00 then σ = 10 pointsT/F
• If σ = 20, a score above the mean
by 10 points will have z = 1.00T/F
18. Learning Check - Answer
• If z = +2 then 2σ = 10 so σ = 5False
• If σ = 20 then z = 10/20 = 0.5False
19. 5.3 Standardizing a Distribution
• Every X value can be transformed to a z-score
• Characteristics of z-score transformation
– Same shape as original distribution
– Mean of z-score distribution is always 0.
– Standard deviation is always 1.00
• A z-score distribution is called a
standardized distribution
24. z-Scores Used for Comparisons
• All z-scores are comparable to each other
• Scores from different distributions can be
converted to z-scores
• z-scores (standardized scores) allow the direct
comparison of scores from two different
distributions because they have been
converted to the same scale
25. 5.4 Other
Standardized Distributions
• Process of standardization is widely used
– SAT has μ = 500 and σ = 100
– IQ has μ = 100 and σ = 15 Points
• Standardizing a distribution has two steps
– Original raw scores transformed to z-scores
– The z-scores are transformed to new X values so
that the specific predetermined μ and σ are
attained.
27. Learning Check
• A score of X=59 comes from a distribution with
μ=63 and σ=8. This distribution is standardized to
a new distribution with μ=50 and σ=10. What is
the new value of the original score?
• 59A
• 45B
• 46C
• 55D
28. Learning Check - Answer
• A score of X=59 comes from a distribution with
μ=63 and σ=8. This distribution is standardized to
a new distribution with μ=50 and σ=10. What is
the new value of the original score?
• 59A
• 45B
• 46C
• 55D
29. 5.5 Computing z-Scores
for a Sample
• Populations are most common context for
computing z-scores
• It is possible to compute z-scores for samples
– Indicates relative position of score in sample
– Indicates distance from sample mean
• Sample distribution can be transformed into
z-scores
– Same shape as original distribution
– Same mean M and standard deviation s
30. 5.6 Looking Ahead to
Inferential Statistics
• Interpretation of research results depends on
determining if (treated) a sample is
“noticeably different” from the population
• One technique for defining “noticeably
different” uses z-scores.
33. Learning Check
• Last week Andi had exams in Chemistry and in Spanish.
On the chemistry exam, the mean was µ = 30 with σ = 5,
and Andi had a score of X = 45. On the Spanish exam, the
mean was µ = 60 with σ = 6 and Andi had a score of X =
65. For which class should Andi expect the better grade?
• ChemistryA
• SpanishB
• There is not enough information to knowC
34. Learning Check - Answer
• Last week Andi had exams in Chemistry and in Spanish.
On the chemistry exam, the mean was µ = 30 with σ = 5,
and Andi had a score of X = 45. On the Spanish exam, the
mean was µ = 60 with σ = 6 and Andi had a score of X =
65. For which class should Andi expect the better grade?
• ChemistryA
• SpanishB
• There is not enough information to knowC
35. Learning Check
• Decide if each of the following statements
is True or False.
• Transforming an entire distribution of
scores into z-scores will not change the
shape of the distribution.
T/F
• If a sample of n = 10 scores is transformed
into z-scores, there will be five positive z-
scores and five negative z-scores.
T/F
36. Learning Check Answer
• Each score location relative to all other
scores is unchanged so the shape of the
distribution is unchanged
True
• Number of z-scores above/below mean
will be exactly the same as number of
original scores above/below mean
False
FIGURE 5.1 Two distributions of exam scores. For both distributions, μ = 70, but for one distribution, σ = 3 and for the other, σ = 12. The relative position of X = 76 is very different for the two distributions.
FIGURE 5.2 The relationship between z-score values and locations in a population distribution.
Remember that z-scores identify a specific location of a score in terms of deviations from the mean and relative to the standard deviation.
Equations 5.1 and 5.2.
FIGURE 5.3 A visual presentation of the question in Example 5.4. If 2 standard deviations correspond to a 6-point distance, then one standard deviation must equal 3 points.
FIGURE 5.4 A visual presentation of the question in Example 5.6. The 12-point distance from 42 to 54 corresponds to 3 standard deviations. Therefore, the standard deviation must be σ = 4. Also, the score X = 42 is below the mean by one standard deviation, so the mean must be μ = 46.
FIGURE 5.5 An entire population of scores is transformed into z-scores. The transformation does not change the shape of the population, but the mean is transformed into a value of 0 and the standard deviation is transformed to a value of 1.
FIGURE 5.6 Following a z-score transformation, the X-axis is relabeled in z-score units. The distance that is equivalent to 1 standard deviation of the X-axis (σ = 10 points in this example) corresponds to 1 point on the z-score scale
FIGURE 5.7 Transforming a distribution of raw scores (a) into z-scores (b) will not change the shape of the distribution.
FIGURE 5.8 The distribution of exam scores from Example 5.7. The original distribution was standardized to produce a new distribution with μ = 50 and σ = 10. Note that each individual is identified by an original score, a z-score, and a new, standardized score. For example, Joe has an original score of 43, a z-score of -1.00, and a standardized score of 40.
FIGURE 5.9 A diagram of a research study. The goal of the study is to evaluate the effect of a treatment. A sample is selected from the populations and the treatment is administered to the sample. If, after treatment, the individuals are noticeably different for the individuals in the original population, then we have evidence that the treatment does have an effect.
FIGURE 5.10 The distribution of weights for the population of adult rats. Note that individuals with z-scores near 0 are typical or representative. However, individuals with z-scores beyond +2.00 and -2.00 are extreme and noticeably different from most of the others in the distribution.