Question Description
I'm working on a mathematics writing question and need an explanation to help me learn.
Sec 4.3
#2 (b) & (c)
#3 (c)
#4 (b) & (c)
#8
#10 ( Hint: Use proof by contradiction. Apply Bolzano-Weirstrass & problem 8 to get contradiction).
Unformatted Attachment Preview
EXERCISES 4.3
1. Prove Theorem 4.3.3.
2. Show that the following functions are not uniformly continuous on the given domain.
1
*a. f(x) = *. Dom f = (0.00)
b. 8(x) Dom g =
c. h(x) = sin Dom h =
(0,00)
x2
(0.00)
3. Prove that each of the following functions is uniformly continuous on the indicated set.
*a. f(x)
x€ [0, …)
b. 8(x) = r?, XEN
.
1 + x
1
c. h(x)
XER d. k(x) = cosx, ER
r? +1'
r
sinx
e. e(x)
x€ (0,00) *l. f(x) = x€ (0, 1)
x + 1
4. Show that each of the following functions is a Lipschitz function.
1
*a. f(x) Dom f = (a,00), a > 0 b. 8(x)
-
X
x
Dom 8 = (0,00)
+1'
ch(x) = sin Dom h = = (a,00), a > 0 d. p(x) a polynomial, Dom p = = (-a, a), a > 0
5. *a. Show that f(x) = Vx satisfies a Lipschitz condition on (a,00), a > 0.
b. Prove that Vx is uniformly continuous on (0.00).
c. Show that f does not satisfy a Lipschitz condition on (0,00).
6. Suppose E C R and f, 8 are Lipschitz functions on E.
a. Prove that f + g is a Lipschitz function on E.
b. If in addition f and g are bounded on E, or the set E is compact, prove that fg is a Lipschitz function on E.
7. Suppose E C R and f, 8 are uniformly continuous real-valued functions on E.
a. Prove that f + g is uniformly continuous on E.
*b. If, in addition, f and g are bounded, prove that fg is uniformly continuous on E.
c. Is part (b) still true if only one of the two functions is bounded?
8. Suppose E CR and f: E-R is uniformly continuous. If {x,} is a Cauchy sequence in E, prove that {f(x.)} is a
Cauchy sequence.
9. Let f:(a,b) → R be uniformly continuous on (a, b). Use the previous exercise to show that f can be defined at a
and b such that f is continuous on (a, b).
10. Suppose that E is a bounded subset of R and f: E-R is uniformly continuous on E. Prove that f is bounded
on E.
4.3
Uniform Continuity
In the previous section we discussed continuity of a function at a point and on a set. By
Definition 4.2.1, a function f:E → R is continuous on E if for each p E E, given any
€ > 0, there exists a 8 > O such that \(x) – f(p)] < e for all x € En Nop). In gen-
eral, for a given e > 0, the choice of 8 that works depends not only on e and the func-
tion f, but also on the point p. This was illustrated in Example 4.1.2(g) for the function
f(x) = 1/x.x € (0,00). Functions for which a choice of 8 independent of p is possible
are given a special name.
4.3.1 DEFINITION Lei ECR and f: E™R. The function is uniformly continuous
on E if given e > 0, there exists a 8 >0 such that
\f(x) – f(y)] 0 be given. Take S = €/2C. If x, y E E with lx – ył < 8, then by the above
\(x) – f(y)] = 2Clx – yl < 2C8 = e.
Therefore, f is uniformly continuous on E. In this example, the choice of 8 depends
both on e and the set E. In the exercises you will be asked to show that this result is
false if the set E is an unbounded interval.
(b) Let f(x) = sin x. As in Example 4.2.2(f),
Vly) – f(x)= ly – x1
for all x, y E R. Consequently, f is uniformly continuous on R.
4.3
Uniform Continuity
145
146
Chapter 4
Limits and Continuity
Proof. Exercise 1. O
(c) In this example we show that the function f(x) = 1/x, x € (0.00) is not uniformly
continuous on (0,00). Suppose, on the contrary, that f is uniformly continuous on
(0,00). Then, as in Example 4.1.2(g), if we take e = 1, there exists a 8 >0 such that
Vix) = f()) = 1*-} 0. Suppose x, y E (a,). Then
THEOREM If KCR is compact and f: K+R is continuous on K, then f is uni-
formly continuous on K.
Proof. Let e > 0 be given. Since f is continuous, for each pe K, there exists a
Op > O such that
\F(x) - f() <
(3)
for all x E KA N28,().
The collection {N$, ()}pek is an open cover of K. Since K is compact, a finite num-
ber of these will cover K. Thus there exist a finite number of points Pos.
such that
., Pn in K
\f(x) – fb)!
=
Fazla yl.
ry
Hence, given e > 0, if we choose & such that 0 < s < a?e, then as a consequence of
the above inequality, \f(x) – f(y)] < e for all x, y E (a,00) with bx – y < 8.
cÚN().
Let
Lipschitz Functions
Both of the functions in Example 4.3.2(a) and (b), and the function f(x) = 1/x with
Dom f = [a, 00), a > 0, are examples of an extensive class of functions. If E CR, a
function f: EnR satisfies a Lipschitz condition on E if there exists a positive con-
stant M such that
\f(x) – f(y)] = Mpx - y
for all x, y E E. Functions satisfying the above inequality are usually referred to as Lip-
schitz functions. As we will see in the next chapter, functions for which the derivative
is bounded are Lipschitz functions. As a consequence of the following theorem, every
Lipschitz function is uniformly continuous. However, not every uniformly continuous
function is a Lipschitz function. For example, the function f(x) = Vr is uniformly
continuous on (0,00), but f does not satisfy a Lipschitz condition on [0, 0) (see Ex-
ercise 5).
8 = min{de, : i = 1,...,n}.
Then 8 > 0. Suppose x, y E K with [x – yl < 8. Since x € K, x € N8,(Pi) for some
i. Furthermore, since fx – yl
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This is a two part paper. Course Project Part I
Required ResourcesRead/review the following resources for this activity: ...
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This is a two part paper. Course Project Part I
Required ResourcesRead/review the following resources for this activity:
Textbook: Chapter 8
Lesson
Scenario/SummaryYou will complete a Course Project in this course that will span two
weeks. The final project is due the Sunday of Week 7. The project is
broken into two parts and it would be most effective to complete Part I
in Week 6 and Part II in Week 7. In Week 6, Confidence Intervals will be explored and in Week 7 Hypothesis testing will be explored.A confidence interval is a defined range of values such that there is
a specified probability that the value of a parameter lies within the
interval.In Part I of this project, you will pick a topic, complete research and provide a write-up that includes calculations. Round all values to two decimal places when appropriate.DeliverablesChoose a Topic where you can gather at least 50 pieces of data. Examples of Topics
The Golden Gate Warriors Points Per Game in 2016 (use the points scored in the first 50 games).
High School Graduation Rates by State (use the graduation rates for all 50 states)
Average Tuition Rates in the US (You have to find the tuition rates of 50 college/universities).
The prices of a hotel room per night in a major city (You have to find the price of the same night of hotels in one city).
Weights of 50 babies at birth.
Write at least a 1-Page ReportOpen a Word Document
Introduction--Provide a description of your topic and cite where you found your data.
Sample Data—Include a 5x10 table including your 50 values in your report. You must provide ALL of your sample data.
Problem Computations—For the topic you chose, you must answer the following:
Determine the mean and standard deviation of your sample.
Find the 80%, 95%, and 99% confidence intervals.
Make sure to list the margin of error for the 80%, 95%, and 99% confidence interval.
Create your own confidence interval (you cannot use 80%, 95%, and
99%) and make sure to show your work. Make sure to list the margin of
error.
Problem Analysis—Write a half-page reflection.
What trend do you see takes place to the confidence interval as the
confidence level rises? Explain mathematically why that takes place.
Provide a sentence for each confidence interval created in part c)
which explains what the confidence interval means in context of topic of
your project.
Explain how Part I of the project has helped you understand confidence intervals better?
How did this project help you understand statistics better?
Required SoftwareMicrosoft Office: Word and ExcelUse a personal copy or access the software at https://application.chamberlain.edu (Links to an external site.).GradingThis activity will be graded based on the Course Project grading rubric. You can view the rubric below.Course Project Rubric
Criteria
Ratings
Pts
Part I: Topic & Introduction
4.0 pts
3.0 ptsAbove Average Student picks appropriate topic and introduces data. No citation.
2.0 ptsAverage. Student does not pick a topic that is appropriate for the project, introduces the data but does not cite source.
1.0 ptsNeeds Improvement Students provides topic without descritption and citation.
0.0 ptsNo Effort. No topic, descritpion or citation is provided.
4.0 pts
Part I: Sample Data
4.0 ptsProficient Student provides ALL 50 pieces of data.
3.0 ptsAbove Average Student provides 30-49 pieces of data.
2.0 ptsAverage Student provides 20 - 29 pieces of data.
1.0 ptsNeeds Improvement Student provides 1-19 pieces of data.
0.0 ptsNo Effort. No Data was provided.
4.0 pts
Part I: Mean & Standard Deviation
5.0 ptsProficient Mean & Sample Standard Deviation of the data set is correct with no rounding error. .
4.0 ptsAbove Average Mean & Sample Standard Deviation of the data set is correct but with roujnding error.
3.0 ptsAverage One Value (either mean or sample standsrd deviation) is correct but the other is not correct.
1.0 ptsNeeds Improvement Both the Mean & Sample Standard Deviation are incorrect but it was attempted.
0.0 ptsNo Effort. The mean and sample standard deviation
5.0 pts
Part I: Constructing the 80%, 95%, 99% Confidence Intervals
15.0 ptsProficient Computes the 80%, 95%, and 99% confidence intervals correclty making sure to note the margin of error for each.
12.0 ptsAbove Average Computes the
80%, 95%, and 99% confidence intervals correclty but is missing margin
of errors (or some of the margin of errors are incorrect).
10.0 ptsAverage Computes the 80%, 95%, and 99% confidence intervals but there are some errors in the calculations.
6.0 ptsNeeds Improvement Computes
the 80%, 95%, and 99% confidence intervals but all of the values are
incorrect. The component was attempted.
0.0 ptsNo Effort. No Confidence Intervals are provided.
15.0 pts
Part I: Creating a new confidence interval
7.0 ptsProficient. Student computes a confidence interval (not 80%, 95%, 99%) correctly making sure to list the margin of error.
5.0 ptsAbove Average. Student
computes a confidence interval (not 80%, 95%, 99%) correctly making sure
to list the margin of error but there is rounding error.
4.0 ptsAverage. Student computes a confidence interval (not 80%, 95%, 99%) correctly but does not highlight the margin of error.
3.0 ptsNeeds Improvement Student computes a confidence interval (not 80%, 95%, 99%) but it was not done correctly.
0.0 ptsNo Effort. The student did not create a new confidence interval.
7.0 pts
Part I: Problem Analysis
10.0 ptsProficient. Student
addresses trend that takes place when the confidence level rises.
Provides a sentence for each confidence interval created explaining what
the confidence interval means in context of the data collected.
Provides a reflection for Part I of the project.
8.0 ptsAbove Average. Student
addresses trend that takes place when the confidence level rises.
Provides sentences for each confidence interval created explaining what
the confience interval means in context of the data collected. Does NOT
provide a Reflection.
7.0 ptsAverage. Student may or may
not address the trend that takes place when the confidence level rises.
Provides a sentence for SOME confidence intervaSl created explaining
what the confidence interval means in context of the data collected. A
reflection Part I of the project may or may not be provided.
5.0 ptsNeeds Improvement. Majority of the analysis is missing.
0.0 ptsNo Effort. No Problem Anaylsis is provided.
10.0 pts
Part II: Choose a Data Set & Preliminary Data
5.0 ptsProficient. Student computes all 4 Preliminary Data Values.
4.0 ptsAbove Average. Student computes all 3 Preliminary Data Values.
3.0 ptsAverage. Student computes all 2 Preliminary Data Values.
1.0 ptsNeeds Improvement. Student computes all 1 Preliminary Data Values.
0.0 ptsNo Effort. No Preliminary Data
5.0 pts
Part II: Hypothesis Testing
20.0 ptsProficient. Completes 4
Hypothesis Tests highlighting the null/alternate hypothesis, value of
test statistic, and report p-value.
16.0 ptsAbove Average. Completes 3
Hypothesis Tests highlighting the null/alternate hypothesis, value of
test statistic, and report p-value.
14.0 ptsAverage. Completes 2 Hypothesis Tests highlighting the null/alternate hypothesis, value of test statistic, and report p-value.
10.0 ptsNeeds Improvement: Completes
1 Hypothesis Test highlighting the null/alternate hypothesis, value of
test statistic, and report p-value.
0.0 ptsNo Effort. No Hypothesis Tests were completed.
20.0 pts
Part II: Hypothesis Testing Analysis
10.0 ptsProficient. State correct conclusion (Reject/Fail to Reject) and valid explanations in context of the data for ALL 4 Problems.
8.0 ptsAbove Average. State correct conclusion (Reject/Fail to Reject) and valid explanations in context of the data for 3 Problems.
7.0 ptsAverage. State correct conclusion (Reject/Fail to Reject) and valid explanations in context of the data for 2 Problems.
5.0 ptsNeeds Improvement. State correct conclusion (Reject/Fail to Reject) and valid explanations in context of the data for 1 Problem
0.0 ptsNo Effort. No conclusion/explanations were given.
10.0 pts
Part II: Proposal and computations for new hypothesis test
10.0 ptsProficient. Student creates
an original Hypothesis Test based on one of the data sets highlighting
the null/alternate hypothesis, value of test statistic, report p-value,
conclusion and explanation.
8.0 ptsProficient. Student creates
an original Hypothesis Test based on one of the data sets correclty and
has MOST of the content: highlighting the null/alternate hypothesis,
value of test statistic, report p-value, conclusion and explanation.
7.0 ptsAverage. Student creates an
original Hypothesis Test based on one of the data sets and MISSING MOST
of the content: highlighting the null/alternate hypothesis, value of
test statistic, report p-value, conclusion and explanation.
5.0 ptsNeeds Improvement. Student
creates an original Hypothesis Test based on one of the data sets but
there are multiple mistakes and/or conclusions are not valid.
0.0 ptsNo Effort. The student did not propose/compute a new hypothesis test.
10.0 pts
Total Points: 90.0
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For this assignment follow the Instructions Below:InstructionsCarefully review the information provided below about the ...
Analyze a Fictitious Statistical Study
For this assignment follow the Instructions Below:InstructionsCarefully review the information provided below about the fictitious study, then address each assignment requirement. Scenario:You are the new director of institutional research at a small state university, and you have been assigned the task of analyzing information for the dean of the School of Education regarding the performance of their undergraduate students on the often-controversial Graduate Record Exam (GRE). Many educators believe the GRE is a poor evaluator of undergraduate performance as well as a poor predictor of graduate school performance. The dean is considering eliminating the GRE from graduate school admissions requirements.The dean has already collected data on four variables: 1) gender, 2) grade point average (GPA), 3) GRE score, and 4) graduate degree completion frequency. Your job is to develop a proposed analysis to assist the dean to make an informed decision regarding the future use of the GRE.Note:(For this assignment, you don’t have to produce any data. This assignment is asking for you to develop the analyses to answer the different questions (see below 1 – 4); relationships questions (What analyses can you use for relationship questions? What types of data (level of measurement)?), for effect questions (What analyses can you use to test for effects of independent variables on dependent variables?) Think on the levels of the independent variables. What types of data (nominal, ordinal, interval, ratio)?), and interaction effects between independent variables. You should also discuss the assumptions of each test. No data is required to be presented. This is similar to a question that you will encounter in your Doctoral Comprehensive Exams. You should provide information that shows your understanding of the different types of analyses, as well as possible outcomes of the analyses. In addition, you have to include in your discussion the possible conclusions based on the possible results; rejecting the null, and not rejecting the null. Using this information, develop the following foundational components for a proposed analysis:A relationship research question involving GPA and GRE scores; corresponding null and alternative hypotheses; the type of statistical analysis to be employed to determine significance; explanations of fictitious outcomes identifying both non-significant and significant relationships as related to both null and alternative hypotheses; and recommendations based on non-significant and significant findings.A relationship research question involving gender, GPA, and GRE scores; corresponding null and alternative hypotheses; the type of statistical analysis to be employed to determine significance; explanations of fictitious outcomes identifying both non-significant and significant relationships as related to both null and alternative hypotheses; and recommendations based on non-significant and significant findings.An effect research question involving gender and GRE scores; corresponding null and alternative hypotheses; the type of statistical analysis to be employed to determine significance; explanations of fictitious outcomes identifying both a non-significant and a significant effect as related to both null and alternative hypotheses; and recommendations based on non-significant and significant findings.An effect research question involving gender, GRE score, and degree completion frequency; corresponding null and alternative hypotheses; the type of statistical analysis to be employed to determine significance; explanations of fictitious outcomes identifying both a non-significant and a significant effect as related to both null and alternative hypotheses; and recommendations based on non-significant and significant findings.Finalize your report with a written analysis of your results and recommendations for the dean based on your findings.Support your assignment with at least five scholarly resources. In addition to these specified resources, other appropriate scholarly resources, including older articles, may be included.Length: 12 pages, not including title and reference pagesattached is a reporting stats in apa style
Level of Confidence as Criteria for Significant Predictors Executive Summary
A marketing company based out of New York City is doing well and is looking to expand internationally. The CEO and VP of ...
Level of Confidence as Criteria for Significant Predictors Executive Summary
A marketing company based out of New York City is doing well and is looking to expand internationally. The CEO and VP of Operations decide to enlist the help of a consulting firm that you work for, to help collect data and analyze market trends. You work for Mercer Human Resources. The Mercer Human Resource Consulting website (www.mercer.com) lists prices of certain items in selected cities around the world. They also report an overall cost-of-living index for each city compared to the costs of hundreds of items in New York City (NYC). For example, London at 88.33 is 11.67% less expensive than NYC.More specifically, if you choose to explore the website further you will find a lot of fun and interesting data. You can explore the website more on your own after the course concludes.https://mobilityexchange.mercer.com/Insights/cost-of-living-rankings#rankingsIn the Excel document, you will find the 2018 data for 17 cities in the data set Cost of Living. Included are the 2018 cost of living index, cost of a 3-bedroom apartment (per month), price of monthly transportation pass, price of a mid-range bottle of wine, price of a loaf of bread (1 lb.), the price of a gallon of milk and price for a 12 oz. cup of black coffee. All prices are in U.S. dollars.You use this information to run a Multiple Linear Regression to predict Cost of living, along with calculating various descriptive statistics. This is given in the Excel output (that is, the MLR has already been calculated. Your task is to interpret the data). Based on this information, in which city should you open a second office in? You must justify your answer. If you want to recommend 2 or 3 different cities and rank them based on the data and your findings, this is fine as well. This should be ¾ to 1 page, no more than 1 single-spaced page in length, using 12-point Times New Roman font. You do not need to do any calculations, but you do need to pick a city to open a second location at and justify your answer based upon the provided results of the Multiple Linear Regression. What is an Executive Summary?Think of this assignment as the first page of a much longer report, known as an Executive Summary, that essentially summarizes your findings briefly and at a high level. This needs to be written up neatly and professionally. This would be something you would present at a board meeting in a corporate environment.To help you make this decision here are some things to consider:Based on the MLR output, what variable(s) is/are significant? From the significant predictors, review the mean, median, min, max, Q1 and Q3 values? It might be a good idea to compare these values to what the New York value is for that variable. Remember New York is the baseline as that is where headquarters are located.Based on the descriptive statistics, for the significant predictors, what city/cities has the best potential? What city or cities fall above or below the median and/or the mean? What city or cities are in the upper 3rd quartile? Or the bottom quartile? These are some things to consider not necessarily questions you need to answer in your Executive Summary. But they are questions to help guide you along in your analysis.Supporting documents:https://edge.apus.edu/access/content/attachment/424212/Assignments/11adcab4-fb2a-41cf-84ac-72e0695762eb/Math%20302%20Final%20Project.xlsx
Graphing and Shifting Trigonometric Functions
Instructions:Your initial post will include five screen shots and four sentences (one sentence for eac ...
Graphing and Shifting Trigonometric Functions
Instructions:Your initial post will include five screen shots and four sentences (one sentence for each of the last four screen shots).Screenshot #1Flip a coin. Your flip will determine the trigonometric function you will be working with for your initial post.Heads = use sineTails = use cosineFor example, if I flipped a tail, my initial post would focus on the trigonometric function cosine.Graph your function and take a screen shot of the graph.You can use any program you like. Here is one option: Illuminations: Trigonometric Graphing.Please refer to the discussion board on how to take screen shots.Graph y=cos(x) ory=sin(x) Your subject line will be cos(x) or sin(x) depending on your flip.Screenshot #2Now, consider this equation. The equation used will depend on your original coin toss.y=Acos(B(x−C))+D y=Asin(B(x−C))+DUsing the Illuminations: Trigonometric Graphing site, figure out what happens when you make A larger (try 1, 2, 3, and 4).Explain in one sentence what happens as you make A larger and tell us what this transformation is called.Then pick an interesting large number (something larger than 1), and graph y=Acos(x) or y=Asin(x)The equation used will depend on your original coin toss.Take a screen shot of your graph and post the equation.Screenshot #3Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make B larger (try 1, 2, 3, and 4) and tell us what this transformation is called.Explain in one sentence what happens as you make B larger.Then pick an interesting large number (something larger than 1), and graph y=cos(Bx) or y=sin(Bx)The equation used will depend on your original coin toss.Take a screen shot of your graph and post the equation.Screenshot #4Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make C larger (try 0, 30 degrees, 45 degrees, and 60 degrees) and tell us what this transformation is called.Explain in one sentence what happens as you make C larger.Then pick an interesting large number (something larger than 0), and graph y=cos(x+C) y=sin(x+C)The equation used will depend on your original coin toss.Take a screen shot of your graph and post the equation.Screenshot #5Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make D larger (try 0, 1, 2, and 3) and tell us what this transformation is called.Explain in one sentence what happens as you make D largerThen pick an interesting large number (something larger than 0), and graph y=cos(x)+D or y=sin(x)+DThe equation used will depend on your original coin toss.Take a screen shot of your graph and post the equation.Response Post:Pick another student’s post who flipped their coin opposite of you.For my example, I would pick someone who flipped heads, or has sin(x) in their subject line.Review the other student’s post.Does each of their answers make sense to you?Explain in at least two sentences why or why not their post makes sense.Please be respectful of other students’ work.Pick two of their transformations (meaning A, B, C, or D and the corresponding graph).What happens when you change the transformation from a positive value to a negative value? For example, if you picked A and D, what happens when you change equations to: y=−Acos(x) or y=−Asin(x)Remember, find the Trig function opposite of yours.What happens when you change the equation to: y=cos(x)−D or y=sin(x)−DPost a screen shot of both transformations together: y=−Acos(x)−D or y=−Asin(x)−D
If log6 2 ≈ 0.3869 and log6 3 ≈ 0.6131, estimate the value of log6 3/2, algebra homework help
If log6 2 ≈ 0.3869 and log6 3 ≈ 0.6131, estimate the value of log6 3/2.A. 0.2262B. 0.6311C. 1D. -0.2262
If log6 2 ≈ 0.3869 and log6 3 ≈ 0.6131, estimate the value of log6 3/2, algebra homework help
If log6 2 ≈ 0.3869 and log6 3 ≈ 0.6131, estimate the value of log6 3/2.A. 0.2262B. 0.6311C. 1D. -0.2262
Chamberlain College of Nursing Chapter 8 Week 7 Confidence Intervals Essay
This is a two part paper. Course Project Part I
Required ResourcesRead/review the following resources for this activity: ...
Chamberlain College of Nursing Chapter 8 Week 7 Confidence Intervals Essay
This is a two part paper. Course Project Part I
Required ResourcesRead/review the following resources for this activity:
Textbook: Chapter 8
Lesson
Scenario/SummaryYou will complete a Course Project in this course that will span two
weeks. The final project is due the Sunday of Week 7. The project is
broken into two parts and it would be most effective to complete Part I
in Week 6 and Part II in Week 7. In Week 6, Confidence Intervals will be explored and in Week 7 Hypothesis testing will be explored.A confidence interval is a defined range of values such that there is
a specified probability that the value of a parameter lies within the
interval.In Part I of this project, you will pick a topic, complete research and provide a write-up that includes calculations. Round all values to two decimal places when appropriate.DeliverablesChoose a Topic where you can gather at least 50 pieces of data. Examples of Topics
The Golden Gate Warriors Points Per Game in 2016 (use the points scored in the first 50 games).
High School Graduation Rates by State (use the graduation rates for all 50 states)
Average Tuition Rates in the US (You have to find the tuition rates of 50 college/universities).
The prices of a hotel room per night in a major city (You have to find the price of the same night of hotels in one city).
Weights of 50 babies at birth.
Write at least a 1-Page ReportOpen a Word Document
Introduction--Provide a description of your topic and cite where you found your data.
Sample Data—Include a 5x10 table including your 50 values in your report. You must provide ALL of your sample data.
Problem Computations—For the topic you chose, you must answer the following:
Determine the mean and standard deviation of your sample.
Find the 80%, 95%, and 99% confidence intervals.
Make sure to list the margin of error for the 80%, 95%, and 99% confidence interval.
Create your own confidence interval (you cannot use 80%, 95%, and
99%) and make sure to show your work. Make sure to list the margin of
error.
Problem Analysis—Write a half-page reflection.
What trend do you see takes place to the confidence interval as the
confidence level rises? Explain mathematically why that takes place.
Provide a sentence for each confidence interval created in part c)
which explains what the confidence interval means in context of topic of
your project.
Explain how Part I of the project has helped you understand confidence intervals better?
How did this project help you understand statistics better?
Required SoftwareMicrosoft Office: Word and ExcelUse a personal copy or access the software at https://application.chamberlain.edu (Links to an external site.).GradingThis activity will be graded based on the Course Project grading rubric. You can view the rubric below.Course Project Rubric
Criteria
Ratings
Pts
Part I: Topic & Introduction
4.0 pts
3.0 ptsAbove Average Student picks appropriate topic and introduces data. No citation.
2.0 ptsAverage. Student does not pick a topic that is appropriate for the project, introduces the data but does not cite source.
1.0 ptsNeeds Improvement Students provides topic without descritption and citation.
0.0 ptsNo Effort. No topic, descritpion or citation is provided.
4.0 pts
Part I: Sample Data
4.0 ptsProficient Student provides ALL 50 pieces of data.
3.0 ptsAbove Average Student provides 30-49 pieces of data.
2.0 ptsAverage Student provides 20 - 29 pieces of data.
1.0 ptsNeeds Improvement Student provides 1-19 pieces of data.
0.0 ptsNo Effort. No Data was provided.
4.0 pts
Part I: Mean & Standard Deviation
5.0 ptsProficient Mean & Sample Standard Deviation of the data set is correct with no rounding error. .
4.0 ptsAbove Average Mean & Sample Standard Deviation of the data set is correct but with roujnding error.
3.0 ptsAverage One Value (either mean or sample standsrd deviation) is correct but the other is not correct.
1.0 ptsNeeds Improvement Both the Mean & Sample Standard Deviation are incorrect but it was attempted.
0.0 ptsNo Effort. The mean and sample standard deviation
5.0 pts
Part I: Constructing the 80%, 95%, 99% Confidence Intervals
15.0 ptsProficient Computes the 80%, 95%, and 99% confidence intervals correclty making sure to note the margin of error for each.
12.0 ptsAbove Average Computes the
80%, 95%, and 99% confidence intervals correclty but is missing margin
of errors (or some of the margin of errors are incorrect).
10.0 ptsAverage Computes the 80%, 95%, and 99% confidence intervals but there are some errors in the calculations.
6.0 ptsNeeds Improvement Computes
the 80%, 95%, and 99% confidence intervals but all of the values are
incorrect. The component was attempted.
0.0 ptsNo Effort. No Confidence Intervals are provided.
15.0 pts
Part I: Creating a new confidence interval
7.0 ptsProficient. Student computes a confidence interval (not 80%, 95%, 99%) correctly making sure to list the margin of error.
5.0 ptsAbove Average. Student
computes a confidence interval (not 80%, 95%, 99%) correctly making sure
to list the margin of error but there is rounding error.
4.0 ptsAverage. Student computes a confidence interval (not 80%, 95%, 99%) correctly but does not highlight the margin of error.
3.0 ptsNeeds Improvement Student computes a confidence interval (not 80%, 95%, 99%) but it was not done correctly.
0.0 ptsNo Effort. The student did not create a new confidence interval.
7.0 pts
Part I: Problem Analysis
10.0 ptsProficient. Student
addresses trend that takes place when the confidence level rises.
Provides a sentence for each confidence interval created explaining what
the confidence interval means in context of the data collected.
Provides a reflection for Part I of the project.
8.0 ptsAbove Average. Student
addresses trend that takes place when the confidence level rises.
Provides sentences for each confidence interval created explaining what
the confience interval means in context of the data collected. Does NOT
provide a Reflection.
7.0 ptsAverage. Student may or may
not address the trend that takes place when the confidence level rises.
Provides a sentence for SOME confidence intervaSl created explaining
what the confidence interval means in context of the data collected. A
reflection Part I of the project may or may not be provided.
5.0 ptsNeeds Improvement. Majority of the analysis is missing.
0.0 ptsNo Effort. No Problem Anaylsis is provided.
10.0 pts
Part II: Choose a Data Set & Preliminary Data
5.0 ptsProficient. Student computes all 4 Preliminary Data Values.
4.0 ptsAbove Average. Student computes all 3 Preliminary Data Values.
3.0 ptsAverage. Student computes all 2 Preliminary Data Values.
1.0 ptsNeeds Improvement. Student computes all 1 Preliminary Data Values.
0.0 ptsNo Effort. No Preliminary Data
5.0 pts
Part II: Hypothesis Testing
20.0 ptsProficient. Completes 4
Hypothesis Tests highlighting the null/alternate hypothesis, value of
test statistic, and report p-value.
16.0 ptsAbove Average. Completes 3
Hypothesis Tests highlighting the null/alternate hypothesis, value of
test statistic, and report p-value.
14.0 ptsAverage. Completes 2 Hypothesis Tests highlighting the null/alternate hypothesis, value of test statistic, and report p-value.
10.0 ptsNeeds Improvement: Completes
1 Hypothesis Test highlighting the null/alternate hypothesis, value of
test statistic, and report p-value.
0.0 ptsNo Effort. No Hypothesis Tests were completed.
20.0 pts
Part II: Hypothesis Testing Analysis
10.0 ptsProficient. State correct conclusion (Reject/Fail to Reject) and valid explanations in context of the data for ALL 4 Problems.
8.0 ptsAbove Average. State correct conclusion (Reject/Fail to Reject) and valid explanations in context of the data for 3 Problems.
7.0 ptsAverage. State correct conclusion (Reject/Fail to Reject) and valid explanations in context of the data for 2 Problems.
5.0 ptsNeeds Improvement. State correct conclusion (Reject/Fail to Reject) and valid explanations in context of the data for 1 Problem
0.0 ptsNo Effort. No conclusion/explanations were given.
10.0 pts
Part II: Proposal and computations for new hypothesis test
10.0 ptsProficient. Student creates
an original Hypothesis Test based on one of the data sets highlighting
the null/alternate hypothesis, value of test statistic, report p-value,
conclusion and explanation.
8.0 ptsProficient. Student creates
an original Hypothesis Test based on one of the data sets correclty and
has MOST of the content: highlighting the null/alternate hypothesis,
value of test statistic, report p-value, conclusion and explanation.
7.0 ptsAverage. Student creates an
original Hypothesis Test based on one of the data sets and MISSING MOST
of the content: highlighting the null/alternate hypothesis, value of
test statistic, report p-value, conclusion and explanation.
5.0 ptsNeeds Improvement. Student
creates an original Hypothesis Test based on one of the data sets but
there are multiple mistakes and/or conclusions are not valid.
0.0 ptsNo Effort. The student did not propose/compute a new hypothesis test.
10.0 pts
Total Points: 90.0
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