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Denote the sets of customers who purchased mysteries as M, science fiction — as S, romance
novels — as R.
It is given that
#𝑀 ∪ 𝑆 ∪ 𝑅 = 68, #𝑀 = 42, #𝑆 = 35, #𝑅 = 25,
#𝑀 ∩ 𝑆 = 19, #𝑀 ∩ 𝑅 ...
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One Way ANOVA
Run a one-way ANOVA using the data File for One-way ANOVA.sav data file.Review the footnotes in the Assignment
Exemplar, ...
One Way ANOVA
Run a one-way ANOVA using the data File for One-way ANOVA.sav data file.Review the footnotes in the Assignment
Exemplar, as they provide additional explanatory information. Consider
how you would extend a quantitative research to be appropriate for a
one-way ANOVA. Will prove the Data File for One-way ANOVA.sav. Must include the following:A description and justification for using the one-way ANOVAA properly formatted research questionA properly formatted H0(null) and H1 (alternate) hypothesisAn APA-formatted “Results” section for the one-way ANOVA
Identification of the statistical testIdentification of independent and dependent variables, including
the identification of the number of levels for the independent variableIdentification of data assumptions and assessment outcomeInferential results in correct APA statistical notation formatA properly formatted box plot
A discussion on how you would extend the one-way ANOVA to a
two-way ANOVA using the variables in the Data File for One-way
ANOVA.sav dataset.Properly APA-formatted referencesAppendix containing SPSS output (see Assignment Exemplar) Will need to cut and paste the SPSS output into the Appendix.SThe SPSS output is not in APA format, so you will need to type the information from the SPSS output to the appropriate sections of the APA table.
If a > 0 and b > 0, which of the following could be an equation of the line graphed in the xy-plane above?, homework help
If a > 0 and b > 0, which of the following could be an equation of the line graphed in the ...
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University of Maryland Global Introduction to Statistics Final Exam
The directions are attach and in bold/red on attached form. The answer sheet is also attached. Work must be shown has stat ...
University of Maryland Global Introduction to Statistics Final Exam
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Design two spinner games. Math homework help
Goals
You will be faced with many situations involving uncertainty
throughout your life, and many of those situations ...
Design two spinner games. Math homework help
Goals
You will be faced with many situations involving uncertainty
throughout your life, and many of those situations will involve money. Whether
you are choosing to buy an insurance policy, a warranty on a printer, or a
chance to win a stuffed teddy bear in a spinner game, it is important that you
understand the mathematics behind these costs.
During this unit, you will design two spinner games.
First you’ll learn about spinner games and choose the
prizes. Then you’ll use expected values to design your games to make a profit
and simulate playing those games to see if they make the profit amount you
expected.
Project Files
You will use the following documents and tools for this
project:
·
Project
Overview: PRM_A_06_project_overview.doc
·
Sample
Project: PRM_A_06_sample_project.ppt
·
Project
Template: PRM_A_06_project_template.ppt
·
Spreadsheet
Template: PRM_A_06_spreadsheet_template.xls
·
Spinner
Tool: Access the Spinner Tool though Student
Resources: Links.
Template
1. Download the project
template and rename the file as GamePresentation_YourName.
This file will become your presentation.
2. Download the spreadsheet template and rename the file as Spreadsheet_YourName. You will use this file to help
you create your presentation.
Project Research
1. Decide on the prize for your first spinner.
·
Look on the Internet to
find an item that sells for less than $5. Prize
ideas include, but are not limited to, small stuffed animals, posters,
T-shirts, goldfish, and small puzzles. Assume that the site you find is the
site where the prizes would be purchased from. If the prizes are sold in bulk
(such as a dozen to a pack), figure out the cost per single prize. Do not use the same item that the sample
project uses.
2. Decide on the prize for your second spinner.
·
Look on the Internet to
find an item that sells for between $10 and $30.
Prize ideas include, but are not limited to, large stuffed animals, sports
caps, board games, and backpacks. Assume that the site you find is the site
where the prizes would be purchased from. Do
not use the same item that the sample project uses.
3. Open your presentation. On slide 1, type your name. On slide 2,
complete the table with prize information.
Project Writing
1. Complete Lesson Checkpoint: Expected Value, an online, ungraded
assessment. You’ll practice finding and interpreting expected value for a game
of chance—a skill essential to completing your project. Reach out to your
teacher with any questions you have after taking this assessment.
2. Design a draft of your first spinner game (the game with the
less expensive prize.)
·
Determine how many sectors
the spinner will have. Choose between 2 and 12 sectors.
·
Choose the cost to play the
game.
·
Tip: You want to make your game appealing to the public. You can
achieve this with a greater probability of winning and/or a lower cost to play.
3. Open your spreadsheet and use the first table in the Expected Values tab to find the expected value of your
game. (Tabs are located at the bottom of the page.)
·
Use the value of your prize
to determine the outcomes. Type the outcomes in cells B5 and C5.
·
Use the number of sectors
in your spinner to determine the probabilities. Type the probabilities in cells
B6 and C6.
·
The expected value will
appear below the table in cell B8. Note: There
is a formula in cell B8. Do not type over it.
4. Think about the expected value shown. Remember, the goal is to
make a profitable game that people will want to play. Modify your game until
you think you have achieved this. You can change the cost to play the game
and/or you can change the number of sectors in your spinner. If you choose to
change your prize, be sure to update the information on slide 2 in your
presentation. Update the values in cells B5, B6, C5, and C6 as needed. Save your work when you are finished.
5. Open your presentation. On slide 3, type in the information about
your first spinner game.
6. Design a draft of your second spinner game (the game with the
more expensive prize.)
·
Determine how many sectors
the spinner will have. Choose between 2 and 12 sectors.
·
Choose the cost to play the
game.
·
Tip: This game has a greater prize value than your first game. To
make the game profitable, you may need to charge more to play the game, and/or
decrease the probability of winning.
7. Open your spreadsheet and use the second table in the Expected Values tab to find the
expected value of your game.
·
Use the value of your prize
to determine the outcomes. Type the outcomes in cells B13 and C13.
·
Use the number of sectors
in your spinner to determine the probabilities. Type the probabilities in cells
B14 and C14.
·
The expected value will appear
below the table in cell B16. Note: There is a
formula in cell B16. Do not type over it.
8. Think about the expected value shown. Remember, the goal is to
make a profitable game that people will want to play. Modify your game until
you think you have achieved this. You can change the cost to play the game
and/or you can change the number of sectors in your spinner. If you choose to
change your prize, be sure to update the information on slide 2 in your
presentation. Update the values in cells B13, B14, C13, and C14 as needed. Save your work when you are finished.
9. Open your presentation. On slide 4, type in the information
about your second spinner game.
10. Complete slide 5 by predicting how much money the game owner,
will make after each spinner game is played 100, 500, and 1000 times.
11. Go to the online spinner. Set it up to model your first spinner.
·
Click Change Spinner. Click
the up and down arrows to adjust the number of sectors to equal the number of
sectors in your first spinner. When finished, click Apply.
12. Simulate playing the game 100, 500, and 1000 times.
·
Predict where the arrow
will land. Consider this sector the winning sector for all plays.
·
With the Number of Spins
set to 100, click Go. Find the number of times, f, the arrow landed in your chosen sector. Record this as the
number of wins in the table below. Calculate the number of losses by subtracting
the number of wins from 100.
·
Change the number of spins
to 400 and click Go. There are now a total of 500 spins. Find the number of
times, f, the arrow landed in your
chosen sector. Record this as the number of wins in the table below. Calculate the
number of losses by subtracting the number of wins from 500.
·
Change the number of spins
to 500 and click Go. There are now a total of 1000 spins. Find the number of
times, f, the arrow landed in your
chosen sector. Record this as the number of wins in the table below. Calculate
the number of losses by subtracting the number of wins from 1000.
Number of plays
Win
Lose
100
500
1000
13. Open your spreadsheet and use the first row of tables in the Simulations tab to calculate the game owner’s profits
from the simulation. Notice that cells for the outcomes are already populated.
·
Use the values from your
table in Step 12 for the frequencies of the outcomes. Type the frequencies in
cells B6 and C6, F6 and G6, and J6 and K6.
·
The profits for the
simulations will appear below the tables in cells B8, F8, and J8. Note: There are formulas in cells B8, F8, and J8. Do
not type over them.
14. Open your presentation. On slide 6, type in the information
about your simulations and compare them to your predictions.
15. Go back to the online spinner. Set it up to model your second
spinner.
·
Click Change Spinner. Click the up and down arrows to adjust
the number of sectors to equal the number of sectors in your first spinner.
When finished, click Apply.
16. Simulate playing the game 100, 500, and 1000 times.
·
Predict where the arrow
will land. Consider this sector the winning sector for all plays.
·
With the Number of Spins
set to 100, click Go. Find the number of times, f, the arrow landed in your
chosen sector. Record this as the number of wins in the table below. Calculate
the number of losses by subtracting the number of wins from 100.
·
Change the number of spins
to 400 and click Go. There are now a total of 500 spins. Find the number of
times, f, the arrow landed in your chosen sector. Record this as the number of
wins in the table below. Calculate the number of losses by subtracting the
number of wins from 500.
·
Change the number of spins
to 500 and click Go. There are now a total of 1000 spins. Find the number of
times, f, the arrow landed in your chosen sector. Record this as the number of
wins in the table below. Calculate the number of losses by subtracting the
number of wins from 1000.
Number of plays
Win
Lose
100
500
1000
17. Open your spreadsheet and use the second row of tables in the Simulations tab to calculate the game owner’s profits
from the simulation. Notice that cells for the outcomes are already populated.
·
Use the values from your
table in Step 16 for the frequencies of the outcomes. Type the frequencies in
cells B14 and C14, F14 and G14, and J14 and K14.
·
The profits for the
simulations will appear below the tables in cells B16, F16, and J16. Note: There are formulas in cells B16, F16, and J16.
Do not type over them.
18. Open your presentation. On slide 7, type in the information
about your simulations and compare them to your predictions.
Project Reflection
1. Join the online session set up for you and your classmates.
2. Write a response to any of the following.
·
Would you be more likely to
play a game with a greater chance of winning a small prize amount or a game
with a lesser chance of winning a large prize amount? Explain.
·
Knowing that games of
chance are designed for the customers to lose, on average, would you save your
money and never play these types of games? Why or why not?
·
What do you think about
consumers buying short-term warranties for brand-new items? Would you be likely
to buy one? Explain.
3. Comment on at least one other student’s post.
Alternate Reflection Assignment
If your teacher excuses you from the online discussion, then
add a slide (slide 8) to the end of your presentation. On the slide, explain
whether, if given the opportunity in the real world, you would play either of
the two games you created, or if you would save your money and walk away. Also,
if you had to choose between the two games, which one would you play and why?
Submission
Confirm that your presentation contains all your work:
·
Prize information for each
spinner game
·
Facts, probability distribution
tables, expected values, and expected value explanations for each spinner game
·
Predicted profits after
100, 500, and 1000 plays of each game
·
Simulation results
(frequency distribution tables and profits) for each game with accompanying
discussion
·
Alternate reflection
assignment slide (ONLY if you did not participate in the online discussion)
Submit your project to your teacher.I ADDED TWO REAL EXAMPLES YOU CAN JUST PARAPHRASE THEMprm_a_06_project_template.pptprm_a_06_sample_project.pptprm_a_06_spreadhseet_template.xlsproject_3_n.pptxproject3.pptx
Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance
As a scholar-practitioner, it is important for you to understand that just because a hypothesis test indicates a relations ...
Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance
As a scholar-practitioner, it is important for you to understand that just because a hypothesis test indicates a relationship exists between an intervention and an outcome, there is a difference between groups, or there is a correlation between two constructs, it does not always provide a default measure for its importance. Although relationships are significant, they can be very minute relationships, very small differences, or very weak correlations. In the end, we need to ask whether the relationships or differences observed are large enough that we should make some practical change in policy or practice.For this Discussion, you will explore statistical significance and meaningfulness.To prepare for this Discussion:Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance.Review Magnusson’s web blog found in the Learning Resources to further your visualization and understanding of statistical power and significance testing.Review the American Statistical Association’s press release and consider the misconceptions and misuse of p-values.Consider the scenario:A research paper claims a meaningful contribution to the literature based on finding statistically significant relationships between predictor and response variables. In the footnotes, you see the following statement, “given this research was exploratory in nature, traditional levels of significance to reject the null hypotheses were relaxed to the .10 level.”By Day 3Post your response to the scenario in which you critically evaluate this footnote. As a reader/reviewer, what response would you provide to the authors about this footnote?Scenarios are listed as follows:
1. The p-value was slightly above conventional threshold, but was described as
“rapidly approaching significance” (i.e., p =.06).
An independent samples t test was used to determine whether student satisfaction
levels in a quantitative reasoning course differed between the traditional classroom
and on-line environments. The samples consisted of students in four face-to-face
classes at a traditional state university (n = 65) and four online classes offered at
the same university (n = 69). Students reported their level of satisfaction on a fivepoint
scale, with higher values indicating higher levels of satisfaction. Since the
study was exploratory in nature, levels of significance were relaxed to the .10 level.
The test was significant t(132) = 1.8, p = .074, wherein students in the face-to-face
class reported lower levels of satisfaction (M = 3.39, SD = 1.8) than did those in the
online sections (M = 3.89, SD = 1.4). We therefore conclude that on average,
students in online quantitative reasoning classes have higher levels of satisfaction.
The results of this study are significant because they provide educators with
evidence of what medium works better in producing quantitatively knowledgeable
practitioners.
2. A results report that does not find any effect and also has small sample size
(possibly no effect detected due to lack of power).
A one-way analysis of variance was used to test whether a relationship exists
between educational attainment and race. The dependent variable of education
was measured as number of years of education completed. The race factor had
three attributes of European American (n = 36), African American (n = 23) and
Hispanic (n = 18). Descriptive statistics indicate that on average, European
Americans have higher levels of education (M = 16.4, SD = 4.6), with African
Americans slightly trailing (M = 15.5, SD = 6.8) and Hispanics having on average
lower levels of educational attainment (M = 13.3, SD = 6.1). The ANOVA was not
significant F (2,74) = 1.789, p = .175, indicating there are no differences in
educational attainment across these three races in the population. The results of
this study are significant because they shed light on the current social conversation
about inequality.
3. Statistical significance is found in a study, but the effect in reality is very small (i.e.,
there was a very minor difference in attitude between men and women). Were the
results meaningful?
An independent samples t test was conducted to determine whether differences
exist between men and women on cultural competency scores. The samples
consisted of 663 women and 650 men taken from a convenience sample of public,
private, and non-profit organizations. Each participant was administered an
instrument that measured his or her current levels of cultural competency. The
© 2016 Laureate Education, Inc. Page 2 of 2
cultural competency score ranges from 0 to 10, with higher scores indicating higher
levels of cultural competency. The descriptive statistics indicate women have
higher levels of cultural competency (M = 9.2, SD = 3.2) than men (M = 8.9, SD =
2.1). The results were significant t (1311) = 2.0, p <.05, indicating that women are
more culturally competent than are men. These results tell us that gender-specific
interventions targeted toward men may assist in bolstering cultural competency.
4. A study has results that seem fine, but there is no clear association to social
change. What is missing?
A correlation test was conducted to determine whether a relationship exists
between level of income and job satisfaction. The sample consisted of 432
employees equally represented across public, private, and non-profit sectors. The
results of the test demonstrate a strong positive correlation between the two
variables, r =.87, p < .01, showing that as level of income increases, job
satisfaction increases as well. Press release as follows:AMERICAN STATISTICAL ASSOCIATION RELEASES STATEMENT ON
STATISTICAL SIGNIFICANCE AND P-VALUES
Provides Principles to Improve the Conduct and Interpretation of Quantitative
Science
March 7, 2016
The American Statistical Association (ASA) has released a “Statement on Statistical Significance
and P-Values” with six principles underlying the proper use and interpretation of the p-value
[http://amstat.tandfonline.com/doi/abs/10.1080/00031305.2016.1154108#.Vt2XIOaE2MN]. The ASA
releases this guidance on p-values to improve the conduct and interpretation of quantitative
science and inform the growing emphasis on reproducibility of science research. The statement
also notes that the increased quantification of scientific research and a proliferation of large,
complex data sets has expanded the scope for statistics and the importance of appropriately
chosen techniques, properly conducted analyses, and correct interpretation.
Good statistical practice is an essential component of good scientific practice, the statement
observes, and such practice “emphasizes principles of good study design and conduct, a variety
of numerical and graphical summaries of data, understanding of the phenomenon under study,
interpretation of results in context, complete reporting and proper logical and quantitative
understanding of what data summaries mean.”
“The p-value was never intended to be a substitute for scientific reasoning,” said Ron
Wasserstein, the ASA’s executive director. “Well-reasoned statistical arguments contain much
more than the value of a single number and whether that number exceeds an arbitrary
threshold. The ASA statement is intended to steer research into a ‘post p<0.05 era.’”
“Over time it appears the p-value has become a gatekeeper for whether work is publishable, at
least in some fields,” said Jessica Utts, ASA president. “This apparent editorial bias leads to the
‘file-drawer effect,’ in which research with statistically significant outcomes are much more
likely to get published, while other work that might well be just as important scientifically is
never seen in print. It also leads to practices called by such names as ‘p-hacking’ and ‘data
dredging’ that emphasize the search for small p-values over other statistical and scientific
reasoning.”
The statement’s six principles, many of which address misconceptions and misuse of the pvalue,
are the following:
1. P-values can indicate how incompatible the data are with a specified statistical model.
2. P-values do not measure the probability that the studied hypothesis is true, or the
probability that the data were produced by random chance alone.
3. Scientific conclusions and business or policy decisions should not be based only on
whether a p-value passes a specific threshold.
4. Proper inference requires full reporting and transparency.
5. A p-value, or statistical significance, does not measure the size of an effect or the
importance of a result.
6. By itself, a p-value does not provide a good measure of evidence regarding a model or
hypothesis.
The statement has short paragraphs elaborating on each principle.
In light of misuses of and misconceptions concerning p-values, the statement notes that
statisticians often supplement or even replace p-values with other approaches. These include
methods “that emphasize estimation over testing such as confidence, credibility, or prediction
intervals; Bayesian methods; alternative measures of evidence such as likelihood ratios or
Bayes factors; and other approaches such as decision-theoretic modeling and false discovery
rates.”
“The contents of the ASA statement and the reasoning behind it are not new—statisticians and
other scientists have been writing on the topic for decades,” Utts said. “But this is the first time
that the community of statisticians, as represented by the ASA Board of Directors, has issued a
statement to address these issues.”
“The issues involved in statistical inference are difficult because inference itself is challenging,”
Wasserstein said. He noted that more than a dozen discussion papers are being published in
the ASA journal The American Statistician with the statement to provide more perspective on
this broad and complex topic. “What we hope will follow is a broad discussion across the
scientific community that leads to a more nuanced approach to interpreting, communicating,
and using the results of statistical methods in research.”
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One Way ANOVA
Run a one-way ANOVA using the data File for One-way ANOVA.sav data file.Review the footnotes in the Assignment
Exemplar, ...
One Way ANOVA
Run a one-way ANOVA using the data File for One-way ANOVA.sav data file.Review the footnotes in the Assignment
Exemplar, as they provide additional explanatory information. Consider
how you would extend a quantitative research to be appropriate for a
one-way ANOVA. Will prove the Data File for One-way ANOVA.sav. Must include the following:A description and justification for using the one-way ANOVAA properly formatted research questionA properly formatted H0(null) and H1 (alternate) hypothesisAn APA-formatted “Results” section for the one-way ANOVA
Identification of the statistical testIdentification of independent and dependent variables, including
the identification of the number of levels for the independent variableIdentification of data assumptions and assessment outcomeInferential results in correct APA statistical notation formatA properly formatted box plot
A discussion on how you would extend the one-way ANOVA to a
two-way ANOVA using the variables in the Data File for One-way
ANOVA.sav dataset.Properly APA-formatted referencesAppendix containing SPSS output (see Assignment Exemplar) Will need to cut and paste the SPSS output into the Appendix.SThe SPSS output is not in APA format, so you will need to type the information from the SPSS output to the appropriate sections of the APA table.
If a > 0 and b > 0, which of the following could be an equation of the line graphed in the xy-plane above?, homework help
If a > 0 and b > 0, which of the following could be an equation of the line graphed in the ...
If a > 0 and b > 0, which of the following could be an equation of the line graphed in the xy-plane above?, homework help
If a > 0 and b > 0, which of the following could be an equation of the line graphed in the xy-plane above?A.y = −ax − bB.y = ax − bC.y = ax + bD.y = −ax + bE.y = abxExplain your answer.
University of Maryland Global Introduction to Statistics Final Exam
The directions are attach and in bold/red on attached form. The answer sheet is also attached. Work must be shown has stat ...
University of Maryland Global Introduction to Statistics Final Exam
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Design two spinner games. Math homework help
Goals
You will be faced with many situations involving uncertainty
throughout your life, and many of those situations ...
Design two spinner games. Math homework help
Goals
You will be faced with many situations involving uncertainty
throughout your life, and many of those situations will involve money. Whether
you are choosing to buy an insurance policy, a warranty on a printer, or a
chance to win a stuffed teddy bear in a spinner game, it is important that you
understand the mathematics behind these costs.
During this unit, you will design two spinner games.
First you’ll learn about spinner games and choose the
prizes. Then you’ll use expected values to design your games to make a profit
and simulate playing those games to see if they make the profit amount you
expected.
Project Files
You will use the following documents and tools for this
project:
·
Project
Overview: PRM_A_06_project_overview.doc
·
Sample
Project: PRM_A_06_sample_project.ppt
·
Project
Template: PRM_A_06_project_template.ppt
·
Spreadsheet
Template: PRM_A_06_spreadsheet_template.xls
·
Spinner
Tool: Access the Spinner Tool though Student
Resources: Links.
Template
1. Download the project
template and rename the file as GamePresentation_YourName.
This file will become your presentation.
2. Download the spreadsheet template and rename the file as Spreadsheet_YourName. You will use this file to help
you create your presentation.
Project Research
1. Decide on the prize for your first spinner.
·
Look on the Internet to
find an item that sells for less than $5. Prize
ideas include, but are not limited to, small stuffed animals, posters,
T-shirts, goldfish, and small puzzles. Assume that the site you find is the
site where the prizes would be purchased from. If the prizes are sold in bulk
(such as a dozen to a pack), figure out the cost per single prize. Do not use the same item that the sample
project uses.
2. Decide on the prize for your second spinner.
·
Look on the Internet to
find an item that sells for between $10 and $30.
Prize ideas include, but are not limited to, large stuffed animals, sports
caps, board games, and backpacks. Assume that the site you find is the site
where the prizes would be purchased from. Do
not use the same item that the sample project uses.
3. Open your presentation. On slide 1, type your name. On slide 2,
complete the table with prize information.
Project Writing
1. Complete Lesson Checkpoint: Expected Value, an online, ungraded
assessment. You’ll practice finding and interpreting expected value for a game
of chance—a skill essential to completing your project. Reach out to your
teacher with any questions you have after taking this assessment.
2. Design a draft of your first spinner game (the game with the
less expensive prize.)
·
Determine how many sectors
the spinner will have. Choose between 2 and 12 sectors.
·
Choose the cost to play the
game.
·
Tip: You want to make your game appealing to the public. You can
achieve this with a greater probability of winning and/or a lower cost to play.
3. Open your spreadsheet and use the first table in the Expected Values tab to find the expected value of your
game. (Tabs are located at the bottom of the page.)
·
Use the value of your prize
to determine the outcomes. Type the outcomes in cells B5 and C5.
·
Use the number of sectors
in your spinner to determine the probabilities. Type the probabilities in cells
B6 and C6.
·
The expected value will
appear below the table in cell B8. Note: There
is a formula in cell B8. Do not type over it.
4. Think about the expected value shown. Remember, the goal is to
make a profitable game that people will want to play. Modify your game until
you think you have achieved this. You can change the cost to play the game
and/or you can change the number of sectors in your spinner. If you choose to
change your prize, be sure to update the information on slide 2 in your
presentation. Update the values in cells B5, B6, C5, and C6 as needed. Save your work when you are finished.
5. Open your presentation. On slide 3, type in the information about
your first spinner game.
6. Design a draft of your second spinner game (the game with the
more expensive prize.)
·
Determine how many sectors
the spinner will have. Choose between 2 and 12 sectors.
·
Choose the cost to play the
game.
·
Tip: This game has a greater prize value than your first game. To
make the game profitable, you may need to charge more to play the game, and/or
decrease the probability of winning.
7. Open your spreadsheet and use the second table in the Expected Values tab to find the
expected value of your game.
·
Use the value of your prize
to determine the outcomes. Type the outcomes in cells B13 and C13.
·
Use the number of sectors
in your spinner to determine the probabilities. Type the probabilities in cells
B14 and C14.
·
The expected value will appear
below the table in cell B16. Note: There is a
formula in cell B16. Do not type over it.
8. Think about the expected value shown. Remember, the goal is to
make a profitable game that people will want to play. Modify your game until
you think you have achieved this. You can change the cost to play the game
and/or you can change the number of sectors in your spinner. If you choose to
change your prize, be sure to update the information on slide 2 in your
presentation. Update the values in cells B13, B14, C13, and C14 as needed. Save your work when you are finished.
9. Open your presentation. On slide 4, type in the information
about your second spinner game.
10. Complete slide 5 by predicting how much money the game owner,
will make after each spinner game is played 100, 500, and 1000 times.
11. Go to the online spinner. Set it up to model your first spinner.
·
Click Change Spinner. Click
the up and down arrows to adjust the number of sectors to equal the number of
sectors in your first spinner. When finished, click Apply.
12. Simulate playing the game 100, 500, and 1000 times.
·
Predict where the arrow
will land. Consider this sector the winning sector for all plays.
·
With the Number of Spins
set to 100, click Go. Find the number of times, f, the arrow landed in your chosen sector. Record this as the
number of wins in the table below. Calculate the number of losses by subtracting
the number of wins from 100.
·
Change the number of spins
to 400 and click Go. There are now a total of 500 spins. Find the number of
times, f, the arrow landed in your
chosen sector. Record this as the number of wins in the table below. Calculate the
number of losses by subtracting the number of wins from 500.
·
Change the number of spins
to 500 and click Go. There are now a total of 1000 spins. Find the number of
times, f, the arrow landed in your
chosen sector. Record this as the number of wins in the table below. Calculate
the number of losses by subtracting the number of wins from 1000.
Number of plays
Win
Lose
100
500
1000
13. Open your spreadsheet and use the first row of tables in the Simulations tab to calculate the game owner’s profits
from the simulation. Notice that cells for the outcomes are already populated.
·
Use the values from your
table in Step 12 for the frequencies of the outcomes. Type the frequencies in
cells B6 and C6, F6 and G6, and J6 and K6.
·
The profits for the
simulations will appear below the tables in cells B8, F8, and J8. Note: There are formulas in cells B8, F8, and J8. Do
not type over them.
14. Open your presentation. On slide 6, type in the information
about your simulations and compare them to your predictions.
15. Go back to the online spinner. Set it up to model your second
spinner.
·
Click Change Spinner. Click the up and down arrows to adjust
the number of sectors to equal the number of sectors in your first spinner.
When finished, click Apply.
16. Simulate playing the game 100, 500, and 1000 times.
·
Predict where the arrow
will land. Consider this sector the winning sector for all plays.
·
With the Number of Spins
set to 100, click Go. Find the number of times, f, the arrow landed in your
chosen sector. Record this as the number of wins in the table below. Calculate
the number of losses by subtracting the number of wins from 100.
·
Change the number of spins
to 400 and click Go. There are now a total of 500 spins. Find the number of
times, f, the arrow landed in your chosen sector. Record this as the number of
wins in the table below. Calculate the number of losses by subtracting the
number of wins from 500.
·
Change the number of spins
to 500 and click Go. There are now a total of 1000 spins. Find the number of
times, f, the arrow landed in your chosen sector. Record this as the number of
wins in the table below. Calculate the number of losses by subtracting the
number of wins from 1000.
Number of plays
Win
Lose
100
500
1000
17. Open your spreadsheet and use the second row of tables in the Simulations tab to calculate the game owner’s profits
from the simulation. Notice that cells for the outcomes are already populated.
·
Use the values from your
table in Step 16 for the frequencies of the outcomes. Type the frequencies in
cells B14 and C14, F14 and G14, and J14 and K14.
·
The profits for the
simulations will appear below the tables in cells B16, F16, and J16. Note: There are formulas in cells B16, F16, and J16.
Do not type over them.
18. Open your presentation. On slide 7, type in the information
about your simulations and compare them to your predictions.
Project Reflection
1. Join the online session set up for you and your classmates.
2. Write a response to any of the following.
·
Would you be more likely to
play a game with a greater chance of winning a small prize amount or a game
with a lesser chance of winning a large prize amount? Explain.
·
Knowing that games of
chance are designed for the customers to lose, on average, would you save your
money and never play these types of games? Why or why not?
·
What do you think about
consumers buying short-term warranties for brand-new items? Would you be likely
to buy one? Explain.
3. Comment on at least one other student’s post.
Alternate Reflection Assignment
If your teacher excuses you from the online discussion, then
add a slide (slide 8) to the end of your presentation. On the slide, explain
whether, if given the opportunity in the real world, you would play either of
the two games you created, or if you would save your money and walk away. Also,
if you had to choose between the two games, which one would you play and why?
Submission
Confirm that your presentation contains all your work:
·
Prize information for each
spinner game
·
Facts, probability distribution
tables, expected values, and expected value explanations for each spinner game
·
Predicted profits after
100, 500, and 1000 plays of each game
·
Simulation results
(frequency distribution tables and profits) for each game with accompanying
discussion
·
Alternate reflection
assignment slide (ONLY if you did not participate in the online discussion)
Submit your project to your teacher.I ADDED TWO REAL EXAMPLES YOU CAN JUST PARAPHRASE THEMprm_a_06_project_template.pptprm_a_06_sample_project.pptprm_a_06_spreadhseet_template.xlsproject_3_n.pptxproject3.pptx
Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance
As a scholar-practitioner, it is important for you to understand that just because a hypothesis test indicates a relations ...
Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance
As a scholar-practitioner, it is important for you to understand that just because a hypothesis test indicates a relationship exists between an intervention and an outcome, there is a difference between groups, or there is a correlation between two constructs, it does not always provide a default measure for its importance. Although relationships are significant, they can be very minute relationships, very small differences, or very weak correlations. In the end, we need to ask whether the relationships or differences observed are large enough that we should make some practical change in policy or practice.For this Discussion, you will explore statistical significance and meaningfulness.To prepare for this Discussion:Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance.Review Magnusson’s web blog found in the Learning Resources to further your visualization and understanding of statistical power and significance testing.Review the American Statistical Association’s press release and consider the misconceptions and misuse of p-values.Consider the scenario:A research paper claims a meaningful contribution to the literature based on finding statistically significant relationships between predictor and response variables. In the footnotes, you see the following statement, “given this research was exploratory in nature, traditional levels of significance to reject the null hypotheses were relaxed to the .10 level.”By Day 3Post your response to the scenario in which you critically evaluate this footnote. As a reader/reviewer, what response would you provide to the authors about this footnote?Scenarios are listed as follows:
1. The p-value was slightly above conventional threshold, but was described as
“rapidly approaching significance” (i.e., p =.06).
An independent samples t test was used to determine whether student satisfaction
levels in a quantitative reasoning course differed between the traditional classroom
and on-line environments. The samples consisted of students in four face-to-face
classes at a traditional state university (n = 65) and four online classes offered at
the same university (n = 69). Students reported their level of satisfaction on a fivepoint
scale, with higher values indicating higher levels of satisfaction. Since the
study was exploratory in nature, levels of significance were relaxed to the .10 level.
The test was significant t(132) = 1.8, p = .074, wherein students in the face-to-face
class reported lower levels of satisfaction (M = 3.39, SD = 1.8) than did those in the
online sections (M = 3.89, SD = 1.4). We therefore conclude that on average,
students in online quantitative reasoning classes have higher levels of satisfaction.
The results of this study are significant because they provide educators with
evidence of what medium works better in producing quantitatively knowledgeable
practitioners.
2. A results report that does not find any effect and also has small sample size
(possibly no effect detected due to lack of power).
A one-way analysis of variance was used to test whether a relationship exists
between educational attainment and race. The dependent variable of education
was measured as number of years of education completed. The race factor had
three attributes of European American (n = 36), African American (n = 23) and
Hispanic (n = 18). Descriptive statistics indicate that on average, European
Americans have higher levels of education (M = 16.4, SD = 4.6), with African
Americans slightly trailing (M = 15.5, SD = 6.8) and Hispanics having on average
lower levels of educational attainment (M = 13.3, SD = 6.1). The ANOVA was not
significant F (2,74) = 1.789, p = .175, indicating there are no differences in
educational attainment across these three races in the population. The results of
this study are significant because they shed light on the current social conversation
about inequality.
3. Statistical significance is found in a study, but the effect in reality is very small (i.e.,
there was a very minor difference in attitude between men and women). Were the
results meaningful?
An independent samples t test was conducted to determine whether differences
exist between men and women on cultural competency scores. The samples
consisted of 663 women and 650 men taken from a convenience sample of public,
private, and non-profit organizations. Each participant was administered an
instrument that measured his or her current levels of cultural competency. The
© 2016 Laureate Education, Inc. Page 2 of 2
cultural competency score ranges from 0 to 10, with higher scores indicating higher
levels of cultural competency. The descriptive statistics indicate women have
higher levels of cultural competency (M = 9.2, SD = 3.2) than men (M = 8.9, SD =
2.1). The results were significant t (1311) = 2.0, p <.05, indicating that women are
more culturally competent than are men. These results tell us that gender-specific
interventions targeted toward men may assist in bolstering cultural competency.
4. A study has results that seem fine, but there is no clear association to social
change. What is missing?
A correlation test was conducted to determine whether a relationship exists
between level of income and job satisfaction. The sample consisted of 432
employees equally represented across public, private, and non-profit sectors. The
results of the test demonstrate a strong positive correlation between the two
variables, r =.87, p < .01, showing that as level of income increases, job
satisfaction increases as well. Press release as follows:AMERICAN STATISTICAL ASSOCIATION RELEASES STATEMENT ON
STATISTICAL SIGNIFICANCE AND P-VALUES
Provides Principles to Improve the Conduct and Interpretation of Quantitative
Science
March 7, 2016
The American Statistical Association (ASA) has released a “Statement on Statistical Significance
and P-Values” with six principles underlying the proper use and interpretation of the p-value
[http://amstat.tandfonline.com/doi/abs/10.1080/00031305.2016.1154108#.Vt2XIOaE2MN]. The ASA
releases this guidance on p-values to improve the conduct and interpretation of quantitative
science and inform the growing emphasis on reproducibility of science research. The statement
also notes that the increased quantification of scientific research and a proliferation of large,
complex data sets has expanded the scope for statistics and the importance of appropriately
chosen techniques, properly conducted analyses, and correct interpretation.
Good statistical practice is an essential component of good scientific practice, the statement
observes, and such practice “emphasizes principles of good study design and conduct, a variety
of numerical and graphical summaries of data, understanding of the phenomenon under study,
interpretation of results in context, complete reporting and proper logical and quantitative
understanding of what data summaries mean.”
“The p-value was never intended to be a substitute for scientific reasoning,” said Ron
Wasserstein, the ASA’s executive director. “Well-reasoned statistical arguments contain much
more than the value of a single number and whether that number exceeds an arbitrary
threshold. The ASA statement is intended to steer research into a ‘post p<0.05 era.’”
“Over time it appears the p-value has become a gatekeeper for whether work is publishable, at
least in some fields,” said Jessica Utts, ASA president. “This apparent editorial bias leads to the
‘file-drawer effect,’ in which research with statistically significant outcomes are much more
likely to get published, while other work that might well be just as important scientifically is
never seen in print. It also leads to practices called by such names as ‘p-hacking’ and ‘data
dredging’ that emphasize the search for small p-values over other statistical and scientific
reasoning.”
The statement’s six principles, many of which address misconceptions and misuse of the pvalue,
are the following:
1. P-values can indicate how incompatible the data are with a specified statistical model.
2. P-values do not measure the probability that the studied hypothesis is true, or the
probability that the data were produced by random chance alone.
3. Scientific conclusions and business or policy decisions should not be based only on
whether a p-value passes a specific threshold.
4. Proper inference requires full reporting and transparency.
5. A p-value, or statistical significance, does not measure the size of an effect or the
importance of a result.
6. By itself, a p-value does not provide a good measure of evidence regarding a model or
hypothesis.
The statement has short paragraphs elaborating on each principle.
In light of misuses of and misconceptions concerning p-values, the statement notes that
statisticians often supplement or even replace p-values with other approaches. These include
methods “that emphasize estimation over testing such as confidence, credibility, or prediction
intervals; Bayesian methods; alternative measures of evidence such as likelihood ratios or
Bayes factors; and other approaches such as decision-theoretic modeling and false discovery
rates.”
“The contents of the ASA statement and the reasoning behind it are not new—statisticians and
other scientists have been writing on the topic for decades,” Utts said. “But this is the first time
that the community of statisticians, as represented by the ASA Board of Directors, has issued a
statement to address these issues.”
“The issues involved in statistical inference are difficult because inference itself is challenging,”
Wasserstein said. He noted that more than a dozen discussion papers are being published in
the ASA journal The American Statistician with the statement to provide more perspective on
this broad and complex topic. “What we hope will follow is a broad discussion across the
scientific community that leads to a more nuanced approach to interpreting, communicating,
and using the results of statistical methods in research.”
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