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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
Statistic using Excel spread sheet/T1-T84 calculator.
The Excel spread sheet and pdf is for Experience 2 Application only.EXPERIENCE 3 ASSISGNMENT Suppose you are representing ...
Statistic using Excel spread sheet/T1-T84 calculator.
The Excel spread sheet and pdf is for Experience 2 Application only.EXPERIENCE 3 ASSISGNMENT Suppose you are representing the employees at a large corporation during contract negotiations. You have a list of the salaries of all the employees at the corporation (The salaries include the many lower level employees and the few high paid management employees) and you plan to find a measure of center (e.g. mean, median, or mode).a. Which measure or center would you use to represent the employees in an effort to support your claim that the average salary of lower level employees is much lower than the national average (for lower level employees) and thus should be increased?meanmodemedianb. Why is this the better choice?Suppose you wish to invest money safely and are trying to decide between stock options in two companies. The average rates of return are the same for both companies but, one company has a much larger standard deviation of its rates of return. a. Which company should you invest in?The company with the smaller standard deviationThe company with the larger standard deviationb. Why is this the better choice? Describe the shape of the distribution for the following and justify your answer:a. The distance people travel to work on a typical day - The horizontal axis is the distance traveled in a person's daily commute. The vertical axis is frequency (number of people with that distance for their daily commute). Shape of distribution:skewed leftuniformskewed rightsymmetricJustification:b. Number of hours of sleep for each night of the week (weekdays only) - The horizontal axis is the day of the week (Monday to Friday) and the vertical axis is the amount of sleep in hours for that night. Shape of distribution:symmetricuniformskewed leftskewed rightJustification:c. Age of first heart attack - The horizontal axis is age. The vertical axis is frequency (number of people who had their first heart attack at that age). The population is people in the US who have had at least one heart attack. Shape of distribution:uniformsymmetricskewed leftskewed rightJustification:d. Scores on the Graduate Requirement Exam - This is a standardized test for people entering graduate school. The horizontal axis would be the person's total score. The vertical axis would be frequency (number of people with that score). The population would be all GRE test takers for a given year. Shape of distribution:symmetricskewed rightuniformskewed leftJustification:EXPERIENCE 2 APPLICATIONYou must use spreadsheet software (e.g. Excel) for this problem. 1. For each state and Washington DC, the percentage of people without health insurance was determined. Given the data set (The file is located in the main Experience folder) create the following using spreadsheet software. Refer to the model/methodology for the desired format. Make sure to use 5-20 classes with a "nice" class width when creating the distribution tables. Make sure to label axes in both graphs. a. Grouped frequency distribution (table) b. Grouped relative frequency distribution (table) c. frequency histogram (graph) d. relative frequency histogram (graph) Submit the completed spreadsheet as a .xls or .xlsx file. 2. A survey of 50 college students was conducted to determine how much weekly income they earned from employment. Given the data set in Applications folder for this experience complete the following. Refer to the model/methodology for the desired format. a. Find the 5 number summary of the data set. Min= Q1= Median= Q3= Max= b. Create a box-plot for the data set using software (Choices include: The boxplot generator linked in the resources area, spreadsheet software, TI-84 (take a picture of your calculator), other software or websites.) Upload your finished file below. Question 2 Part 6 of 9Choose File No file chosen c. Identify any outliers. List the individual numbers that are outliers for this data set. If there are multiple outliers, separate them by commas. d. Give a possible explanation as to why the individual (or individuals) from part c might have a number (or numbers) that are so high (or so low). e. Interpret yourself as a percentile in the data set. First estimate your weekly income from employment (If you are not employed then use 0). Then find the percentile (see book for the formula) for your income using the sample data. Then interpret the percentile using the definition and writing a complete sentence.
7 pages
20201114035707chapter5
5.3 Assume that a radiologist group practice has the following cost structure: Furthermore, assume that the group expects ...
20201114035707chapter5
5.3 Assume that a radiologist group practice has the following cost structure: Furthermore, assume that the group expects to perform 7,500 procedures ...
Statistics Discussion
A federal government agency that is responsible for setting vehicle fuel economy standards for automobile manufacturers is ...
Statistics Discussion
A federal government agency that is responsible for setting vehicle fuel economy standards for automobile manufacturers is conducting research in order to update its fuel economy standards for the year 2030. Automobile manufacturers, and consumers, are highly interested in what the agency's findings and determinations will be as this will affect every vehicle in the United States. The federal government agency is very interested in the relationship between the weight of a vehicle and the vehicle's fuel economy (average miles per gallon (MPG)). Specifically, the agency is concerned that if the current trend of automobile manufacturers producing heavier new vehicles continues that its fuel economy targets will not be met. The agency's research department recently collected data for analysis in order to support the agency's upcoming discussion with the industry regarding its proposed 2030 fuel economy standards. The average MPG from a random sample of 750 vehicles was recently calculated by the agency. The research division also collected the vehicle weight of these 750 randomly sampled vehicles. The Vehicle Number, Type, Vehicle Weight, Average MPG, Fuel Tank Size (Gallons), Engine Size (Liters), and Meet or Not Meet Current Standards data were collected for these 750 vehicles. 1. Agency leadership is interested in analyzing the engine sizes of this sample of 750 vehicles. (Use the mean and standard deviation of the Engine Size (L) data. Also, if appropriate based upon your visual analysis of a histogram of the Engine Size (L) data, use the Normal distribution to answer this question.) ROUND TO TWO DECIMAL PLACES-Calculate the probability of randomly selecting a vehicle with an engine size less than 2.7 L.-Calculate the probability of randomly selecting a vehicle with an engine size greater than 3.9 L.-Calculate the probability of randomly selecting a vehicle with an engine between 3.1 L and 4.2 L.-Calculate the engine size that represents the 10th percentile of this sample.2. Agency leadership is very interested in trend analysis. Using the 750 randomly selected vehicles as their sample, data were collected to determine which vehicles currently meet or exceed fuel economy standards and which vehicles currently do not meet fuel economy standards. This information is found in the Meet or Not Meet Current Standards column. Agency leadership asks your team to construct a 95% One-Sample proportion confidence interval for the population proportion of all vehicles that meet current fuel economy standards. Assume that all necessary Central Limit Theorem conditions for a One-Proportion confidence interval have been met.-What is the 95% lower limit?-What is the 95% upper limit?-Using the 95% confidence interval, would it be plausible to conclude that the population proportion of vehicles that currently meet fuel economy standards is 90%?A. No, since 90% lies within the constructed confidence interval.B. Yes, since 90% lies within the constructed confidence interval.C. No, since 90% lies outside the constructed confidence interval.D. Yes, since 90% lies outside the constructed confidence interval.3. Agency leadership decides to run a One Proportion hypothesis test to determine if the proportion of all vehicles that meet or exceed current fuel economy standards is less than 90%. Assume that all necessary Central Limit Theorem conditions for a One-Proportion Z-test have been met.-What is the appropriate null hypothesis in this case? The proportion of all vehicles that meet or exceed current fuel economy standards is, less than, not equal to, greater than, or equal to, 90%.-What is the appropriate alternative hypothesis in this case? The proportion of all vehicles that meet or exceed current fuel economy standards is, less than, greater than, not equal to, or equal to, 90%.-What is the test statistic for this hypothesis test? The test statistic is-What is the p-value for this hypothesis test? The p-value is-What would you conclude based on an α=0.05 level?We, fail to reject or reject, the null hypothesis and, do not accept or accept, the alternative hypothesis since there,is not or is, sufficient evidence that the proportion of all vehicles that meet or exceed current fuel economy standards is, greater or less, than 90% due to the p-value being, greater or less, than the α level.-Explain the results of your hypothesis test. What does the p-value signify? Would you say the observed outcome was unusual? If so, how unusual was the outcome?4. Agency leadership decides to use the vehicle weight data from its random sample of 750 vehicles to estimate the mean vehicle weight of all passenger vehicles currently on the road. Construct a 95% One-Sample T confidence interval for the mean vehicle weight of all passenger vehicles currently on the road. Assume that all necessary Central Limit Theorem conditions for a One-Sample T confidence interval have been met.-What is the 95% lower limit?-What is the 95% upper limit?- Using the 95% confidence interval, would it be plausible to conclude that the mean vehicle weight of all passenger vehicles currently on the road is 2500 pounds?A. No, since 2500 lies within the constructed confidence intervalB. Yes, since 2500 lies outside the constructed confidence interval.C. Yes, since 2500 lies within the constructed confidence interval.D. No, since 2500 lies outside the constructed confidence interval.-Explain why the agency would construct a confidence interval instead of collecting vehicle weight information of all passenger vehicles currently on the road.5. Agency leadership decides to use the vehicle weight data from its random sample of 750 vehicles to estimate the mean vehicle weight of all passenger vehicles currently on the road. Construct a 90% One-Sample T confidence interval for the mean vehicle weight of all passenger vehicles currently on the road. Assume that all necessary Central Limit Theorem conditions for a One-Sample T confidence interval have been met.-What is the 90% lower limit?-What is the 90% upper limit?-Using the 90% confidence interval, would it be plausible to conclude that the mean vehicle weight of all passenger vehicles currently on the road is 2400 pounds?A. No, since 2400 lies outside the constructed confidence interval.B. Yes, since 2400 lies within the constructed confidence intervalC. Yes, since 2400 lies outside the constructed confidence interval.D. No, since 2400 lies within the constructed confidence interval.-Compare your 90% confidence interval to the 95% confidence interval, (2484.92, 2569.56). Explain which confidence interval is wider and why.6. Agency leadership decides to run a One Sample-T hypothesis test to determine if the mean vehicle weight of all passenger vehicles currently on the road is significantly different than 2600 pounds. Assume that all necessary Central Limit Theorem conditions for a One-Sample T-test have been met.-What is the appropriate null hypothesis in this case? The mean vehicle weight of all passenger vehicles currently on the road is, less than, greater than, or equal to, 2600 pounds.-What is the appropriate alternative hypothesis in this case? The mean vehicle weight of all passenger vehicles currently on the road is, greater than, not equal to, equal to, or less than, 2600 pounds.-What is the test statistic for this hypothesis test? The test statistic is-What is the p-value for this hypothesis test? The p-value is-What would you conclude based on an α=0.05 level? We, reject or fail to reject, the null hypothesis and, accept or do not accept, the alternative hypothesis since there, is or is not, sufficient evidence that the mean vehicle weight of all passenger vehicles currently on the road is, not equal to or equal to, 2600 pounds due to the p-value being, greater or less, than the α level.-Based upon your hypothesis test, was the observed outcome unusual? If so, how unusual was the outcome?
University of Alaska Anchorage Random Sampling Error Worksheet
The goal of this assignment is to help you understand the logic underlying the estimation of RSE (Random Sampling Error) b ...
University of Alaska Anchorage Random Sampling Error Worksheet
The goal of this assignment is to help you understand the logic underlying the estimation of RSE (Random Sampling Error) based on simulated computation (estimation) using height data. See Excel Sheet 1 on Excel contains 1620 people’s height data These 1620 people’s height are 54 sets of 30 samples – this means that sample size(n) is 30 and you have 54 of them. Therefore, in this assignment we make following assumptions: Height data of 1620 people (54 sets of samples containing 30 people’s height) are population (I know this actually is a set of sample, but we pretend that this is a population: N = 1620) 30 people’s height within each set of sample is a set of sample: therefore sample size is 30 (n n=30) and there are 54 sets of samples. Based on these assumptions, please compute: Population mean (mean of the 1620 people’s height) Sample mean (mean of the 30 people) – please choose a specific sample from 54 samples, and compute the sample mean based on 30 samples in that particular set.Population standard deviation based on 1620 people as population Sample standard deviation (population standard deviation estimated based on your own sample of 30 – so you need to compute the SD on 30 people’s height in your own sample that you chose) Create a sampling distribution of the mean based on these 54 sets of samples and compare the shape (characteristics) of the sampling distribution with population distribution of height that I provided (sheet 2 grouped frequency polygon) by following these steps: Then step 1 compute the mean of 30 people’s height for each of all the 54 sets of samples – so you need 54 sample means for 54 sets of sample step 2 create a group frequency distribution table based on the computed means (54) – this is a grouped frequency table for sampling distribution of the 54 means Compare the shape of frequency distributions between Population of Height (one I provided) and Sampling distribution of the means (54 sets of Means you created). For your reference I am providing the grouped frequency polygon representing the population distribution (the third sheet of the excel) and answer the following questions: What is the relation between population mean and the mean of the 54 means? – same or differentWhich of the two distributions (population distribution of 1620 height data vs sampling distribution of the 54 means) has a narrower distribution clustered around the population mean? to what extent, the observation of the above two (a and b) aspects of the sampling distribution lend support to the Central Limit Theorem? – this requires you read CLM and understand it. RSE as difference between your own sample mean and the mean of the sampling distribution of mean (average of the 54 sets of sample mean)RSE as Standard Error of the Mean which is the Standard Deviation computed based on sampling distribution of the mean – this means computing a SD based on 54 sample means. For this use the sampling distribution of the mean that you created in the above (you need to use population St Dev computation function in Excel – see below). RSE as Standard Error of the Mean approximated by population standard deviation (based on 1620 data) divided by the square root of n (n=30) RSE as Standard Error of the Mean approximated by sample standard deviation (based on your own sample of n=30) (use of n-1 in denominator – sample standard deviation in Excel – see below) divided by the square root of n (n=30)(This is a bonus point of 5 on top of 30) I assume that 6-3 and 6-4 are different even though they are supposed to be similar according to the lecture. Speculate on the reason why they are different.Based on what you have learned on the four different approaches of estimating RSE, they should be the same. But they are different in this one. Why? Hint: the nature of the sample (30 people’s height)? You can include any questions or comments based on this process. Your points is not entirely based on whether your answer is correct; it is mainly based on evidence of THINKING you put here. 6 ) Estimate the Random Sampling Error in the following four different ways based on your understanding of the definition of RSE we just covered in the class: In computing Means and SD, use excel’s computational functions: For mean (average) see: https://www.youtube.com/watch?v=5_OHS-18RbU\ For standard deviation see: https://www.youtube.com/watch?v=uZWQXQG37Zs There are STD. P (population where the denominator is n) and STD.S (sample where the denominator is n-1). Be careful to use appropriate one. You should, by now, know which one to use when. If you have question on this, please send me an email. In sum your assignment needs to address all these questions Population mean Sample mean Population standard deviation Sample standard deviation (population standard deviation estimated based on your own sample) RSE as difference between your sample mean and the mean of the sampling distribution of mean (average of the 54 sets of sample mean) RSE as Standard Error of the Mean which is Standard Deviation computed on the sampling distribution of the mean. RSE as Standard Error of the Mean approximated by population standard deviation divided by the square root of n (n=30) RSE as Standard Error of the Mean approximated by sample standard deviationofyour own sample) divided by the square root of n (n=30)(bonus points) consideration of why 6-3 and 6-4 are different. 5-aWhat is the relation between population mean and the mean of the 54 means? 5-b. Which of the two distributions (population vs sampling distribution of the means) has a narrower distribution clustered around the population mean? 5-c.To what extent, the observation of the above two (a and b) aspect of the sampling distribution lend support to the Central Limit Theorem?
Statistical Significance and Meaningfulness
For this Discussion, you will explore statistical significance and meaningfulnessReview the American Statistical Associati ...
Statistical Significance and Meaningfulness
For this Discussion, you will explore statistical significance and meaningfulnessReview 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."Post 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? 500 words or more
Be sure to support your Main Post and Response Post with reference to the week’s Learning Resources and other scholarly evidence in APA Style.
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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
Statistic using Excel spread sheet/T1-T84 calculator.
The Excel spread sheet and pdf is for Experience 2 Application only.EXPERIENCE 3 ASSISGNMENT Suppose you are representing ...
Statistic using Excel spread sheet/T1-T84 calculator.
The Excel spread sheet and pdf is for Experience 2 Application only.EXPERIENCE 3 ASSISGNMENT Suppose you are representing the employees at a large corporation during contract negotiations. You have a list of the salaries of all the employees at the corporation (The salaries include the many lower level employees and the few high paid management employees) and you plan to find a measure of center (e.g. mean, median, or mode).a. Which measure or center would you use to represent the employees in an effort to support your claim that the average salary of lower level employees is much lower than the national average (for lower level employees) and thus should be increased?meanmodemedianb. Why is this the better choice?Suppose you wish to invest money safely and are trying to decide between stock options in two companies. The average rates of return are the same for both companies but, one company has a much larger standard deviation of its rates of return. a. Which company should you invest in?The company with the smaller standard deviationThe company with the larger standard deviationb. Why is this the better choice? Describe the shape of the distribution for the following and justify your answer:a. The distance people travel to work on a typical day - The horizontal axis is the distance traveled in a person's daily commute. The vertical axis is frequency (number of people with that distance for their daily commute). Shape of distribution:skewed leftuniformskewed rightsymmetricJustification:b. Number of hours of sleep for each night of the week (weekdays only) - The horizontal axis is the day of the week (Monday to Friday) and the vertical axis is the amount of sleep in hours for that night. Shape of distribution:symmetricuniformskewed leftskewed rightJustification:c. Age of first heart attack - The horizontal axis is age. The vertical axis is frequency (number of people who had their first heart attack at that age). The population is people in the US who have had at least one heart attack. Shape of distribution:uniformsymmetricskewed leftskewed rightJustification:d. Scores on the Graduate Requirement Exam - This is a standardized test for people entering graduate school. The horizontal axis would be the person's total score. The vertical axis would be frequency (number of people with that score). The population would be all GRE test takers for a given year. Shape of distribution:symmetricskewed rightuniformskewed leftJustification:EXPERIENCE 2 APPLICATIONYou must use spreadsheet software (e.g. Excel) for this problem. 1. For each state and Washington DC, the percentage of people without health insurance was determined. Given the data set (The file is located in the main Experience folder) create the following using spreadsheet software. Refer to the model/methodology for the desired format. Make sure to use 5-20 classes with a "nice" class width when creating the distribution tables. Make sure to label axes in both graphs. a. Grouped frequency distribution (table) b. Grouped relative frequency distribution (table) c. frequency histogram (graph) d. relative frequency histogram (graph) Submit the completed spreadsheet as a .xls or .xlsx file. 2. A survey of 50 college students was conducted to determine how much weekly income they earned from employment. Given the data set in Applications folder for this experience complete the following. Refer to the model/methodology for the desired format. a. Find the 5 number summary of the data set. Min= Q1= Median= Q3= Max= b. Create a box-plot for the data set using software (Choices include: The boxplot generator linked in the resources area, spreadsheet software, TI-84 (take a picture of your calculator), other software or websites.) Upload your finished file below. Question 2 Part 6 of 9Choose File No file chosen c. Identify any outliers. List the individual numbers that are outliers for this data set. If there are multiple outliers, separate them by commas. d. Give a possible explanation as to why the individual (or individuals) from part c might have a number (or numbers) that are so high (or so low). e. Interpret yourself as a percentile in the data set. First estimate your weekly income from employment (If you are not employed then use 0). Then find the percentile (see book for the formula) for your income using the sample data. Then interpret the percentile using the definition and writing a complete sentence.
7 pages
20201114035707chapter5
5.3 Assume that a radiologist group practice has the following cost structure: Furthermore, assume that the group expects ...
20201114035707chapter5
5.3 Assume that a radiologist group practice has the following cost structure: Furthermore, assume that the group expects to perform 7,500 procedures ...
Statistics Discussion
A federal government agency that is responsible for setting vehicle fuel economy standards for automobile manufacturers is ...
Statistics Discussion
A federal government agency that is responsible for setting vehicle fuel economy standards for automobile manufacturers is conducting research in order to update its fuel economy standards for the year 2030. Automobile manufacturers, and consumers, are highly interested in what the agency's findings and determinations will be as this will affect every vehicle in the United States. The federal government agency is very interested in the relationship between the weight of a vehicle and the vehicle's fuel economy (average miles per gallon (MPG)). Specifically, the agency is concerned that if the current trend of automobile manufacturers producing heavier new vehicles continues that its fuel economy targets will not be met. The agency's research department recently collected data for analysis in order to support the agency's upcoming discussion with the industry regarding its proposed 2030 fuel economy standards. The average MPG from a random sample of 750 vehicles was recently calculated by the agency. The research division also collected the vehicle weight of these 750 randomly sampled vehicles. The Vehicle Number, Type, Vehicle Weight, Average MPG, Fuel Tank Size (Gallons), Engine Size (Liters), and Meet or Not Meet Current Standards data were collected for these 750 vehicles. 1. Agency leadership is interested in analyzing the engine sizes of this sample of 750 vehicles. (Use the mean and standard deviation of the Engine Size (L) data. Also, if appropriate based upon your visual analysis of a histogram of the Engine Size (L) data, use the Normal distribution to answer this question.) ROUND TO TWO DECIMAL PLACES-Calculate the probability of randomly selecting a vehicle with an engine size less than 2.7 L.-Calculate the probability of randomly selecting a vehicle with an engine size greater than 3.9 L.-Calculate the probability of randomly selecting a vehicle with an engine between 3.1 L and 4.2 L.-Calculate the engine size that represents the 10th percentile of this sample.2. Agency leadership is very interested in trend analysis. Using the 750 randomly selected vehicles as their sample, data were collected to determine which vehicles currently meet or exceed fuel economy standards and which vehicles currently do not meet fuel economy standards. This information is found in the Meet or Not Meet Current Standards column. Agency leadership asks your team to construct a 95% One-Sample proportion confidence interval for the population proportion of all vehicles that meet current fuel economy standards. Assume that all necessary Central Limit Theorem conditions for a One-Proportion confidence interval have been met.-What is the 95% lower limit?-What is the 95% upper limit?-Using the 95% confidence interval, would it be plausible to conclude that the population proportion of vehicles that currently meet fuel economy standards is 90%?A. No, since 90% lies within the constructed confidence interval.B. Yes, since 90% lies within the constructed confidence interval.C. No, since 90% lies outside the constructed confidence interval.D. Yes, since 90% lies outside the constructed confidence interval.3. Agency leadership decides to run a One Proportion hypothesis test to determine if the proportion of all vehicles that meet or exceed current fuel economy standards is less than 90%. Assume that all necessary Central Limit Theorem conditions for a One-Proportion Z-test have been met.-What is the appropriate null hypothesis in this case? The proportion of all vehicles that meet or exceed current fuel economy standards is, less than, not equal to, greater than, or equal to, 90%.-What is the appropriate alternative hypothesis in this case? The proportion of all vehicles that meet or exceed current fuel economy standards is, less than, greater than, not equal to, or equal to, 90%.-What is the test statistic for this hypothesis test? The test statistic is-What is the p-value for this hypothesis test? The p-value is-What would you conclude based on an α=0.05 level?We, fail to reject or reject, the null hypothesis and, do not accept or accept, the alternative hypothesis since there,is not or is, sufficient evidence that the proportion of all vehicles that meet or exceed current fuel economy standards is, greater or less, than 90% due to the p-value being, greater or less, than the α level.-Explain the results of your hypothesis test. What does the p-value signify? Would you say the observed outcome was unusual? If so, how unusual was the outcome?4. Agency leadership decides to use the vehicle weight data from its random sample of 750 vehicles to estimate the mean vehicle weight of all passenger vehicles currently on the road. Construct a 95% One-Sample T confidence interval for the mean vehicle weight of all passenger vehicles currently on the road. Assume that all necessary Central Limit Theorem conditions for a One-Sample T confidence interval have been met.-What is the 95% lower limit?-What is the 95% upper limit?- Using the 95% confidence interval, would it be plausible to conclude that the mean vehicle weight of all passenger vehicles currently on the road is 2500 pounds?A. No, since 2500 lies within the constructed confidence intervalB. Yes, since 2500 lies outside the constructed confidence interval.C. Yes, since 2500 lies within the constructed confidence interval.D. No, since 2500 lies outside the constructed confidence interval.-Explain why the agency would construct a confidence interval instead of collecting vehicle weight information of all passenger vehicles currently on the road.5. Agency leadership decides to use the vehicle weight data from its random sample of 750 vehicles to estimate the mean vehicle weight of all passenger vehicles currently on the road. Construct a 90% One-Sample T confidence interval for the mean vehicle weight of all passenger vehicles currently on the road. Assume that all necessary Central Limit Theorem conditions for a One-Sample T confidence interval have been met.-What is the 90% lower limit?-What is the 90% upper limit?-Using the 90% confidence interval, would it be plausible to conclude that the mean vehicle weight of all passenger vehicles currently on the road is 2400 pounds?A. No, since 2400 lies outside the constructed confidence interval.B. Yes, since 2400 lies within the constructed confidence intervalC. Yes, since 2400 lies outside the constructed confidence interval.D. No, since 2400 lies within the constructed confidence interval.-Compare your 90% confidence interval to the 95% confidence interval, (2484.92, 2569.56). Explain which confidence interval is wider and why.6. Agency leadership decides to run a One Sample-T hypothesis test to determine if the mean vehicle weight of all passenger vehicles currently on the road is significantly different than 2600 pounds. Assume that all necessary Central Limit Theorem conditions for a One-Sample T-test have been met.-What is the appropriate null hypothesis in this case? The mean vehicle weight of all passenger vehicles currently on the road is, less than, greater than, or equal to, 2600 pounds.-What is the appropriate alternative hypothesis in this case? The mean vehicle weight of all passenger vehicles currently on the road is, greater than, not equal to, equal to, or less than, 2600 pounds.-What is the test statistic for this hypothesis test? The test statistic is-What is the p-value for this hypothesis test? The p-value is-What would you conclude based on an α=0.05 level? We, reject or fail to reject, the null hypothesis and, accept or do not accept, the alternative hypothesis since there, is or is not, sufficient evidence that the mean vehicle weight of all passenger vehicles currently on the road is, not equal to or equal to, 2600 pounds due to the p-value being, greater or less, than the α level.-Based upon your hypothesis test, was the observed outcome unusual? If so, how unusual was the outcome?
University of Alaska Anchorage Random Sampling Error Worksheet
The goal of this assignment is to help you understand the logic underlying the estimation of RSE (Random Sampling Error) b ...
University of Alaska Anchorage Random Sampling Error Worksheet
The goal of this assignment is to help you understand the logic underlying the estimation of RSE (Random Sampling Error) based on simulated computation (estimation) using height data. See Excel Sheet 1 on Excel contains 1620 people’s height data These 1620 people’s height are 54 sets of 30 samples – this means that sample size(n) is 30 and you have 54 of them. Therefore, in this assignment we make following assumptions: Height data of 1620 people (54 sets of samples containing 30 people’s height) are population (I know this actually is a set of sample, but we pretend that this is a population: N = 1620) 30 people’s height within each set of sample is a set of sample: therefore sample size is 30 (n n=30) and there are 54 sets of samples. Based on these assumptions, please compute: Population mean (mean of the 1620 people’s height) Sample mean (mean of the 30 people) – please choose a specific sample from 54 samples, and compute the sample mean based on 30 samples in that particular set.Population standard deviation based on 1620 people as population Sample standard deviation (population standard deviation estimated based on your own sample of 30 – so you need to compute the SD on 30 people’s height in your own sample that you chose) Create a sampling distribution of the mean based on these 54 sets of samples and compare the shape (characteristics) of the sampling distribution with population distribution of height that I provided (sheet 2 grouped frequency polygon) by following these steps: Then step 1 compute the mean of 30 people’s height for each of all the 54 sets of samples – so you need 54 sample means for 54 sets of sample step 2 create a group frequency distribution table based on the computed means (54) – this is a grouped frequency table for sampling distribution of the 54 means Compare the shape of frequency distributions between Population of Height (one I provided) and Sampling distribution of the means (54 sets of Means you created). For your reference I am providing the grouped frequency polygon representing the population distribution (the third sheet of the excel) and answer the following questions: What is the relation between population mean and the mean of the 54 means? – same or differentWhich of the two distributions (population distribution of 1620 height data vs sampling distribution of the 54 means) has a narrower distribution clustered around the population mean? to what extent, the observation of the above two (a and b) aspects of the sampling distribution lend support to the Central Limit Theorem? – this requires you read CLM and understand it. RSE as difference between your own sample mean and the mean of the sampling distribution of mean (average of the 54 sets of sample mean)RSE as Standard Error of the Mean which is the Standard Deviation computed based on sampling distribution of the mean – this means computing a SD based on 54 sample means. For this use the sampling distribution of the mean that you created in the above (you need to use population St Dev computation function in Excel – see below). RSE as Standard Error of the Mean approximated by population standard deviation (based on 1620 data) divided by the square root of n (n=30) RSE as Standard Error of the Mean approximated by sample standard deviation (based on your own sample of n=30) (use of n-1 in denominator – sample standard deviation in Excel – see below) divided by the square root of n (n=30)(This is a bonus point of 5 on top of 30) I assume that 6-3 and 6-4 are different even though they are supposed to be similar according to the lecture. Speculate on the reason why they are different.Based on what you have learned on the four different approaches of estimating RSE, they should be the same. But they are different in this one. Why? Hint: the nature of the sample (30 people’s height)? You can include any questions or comments based on this process. Your points is not entirely based on whether your answer is correct; it is mainly based on evidence of THINKING you put here. 6 ) Estimate the Random Sampling Error in the following four different ways based on your understanding of the definition of RSE we just covered in the class: In computing Means and SD, use excel’s computational functions: For mean (average) see: https://www.youtube.com/watch?v=5_OHS-18RbU\ For standard deviation see: https://www.youtube.com/watch?v=uZWQXQG37Zs There are STD. P (population where the denominator is n) and STD.S (sample where the denominator is n-1). Be careful to use appropriate one. You should, by now, know which one to use when. If you have question on this, please send me an email. In sum your assignment needs to address all these questions Population mean Sample mean Population standard deviation Sample standard deviation (population standard deviation estimated based on your own sample) RSE as difference between your sample mean and the mean of the sampling distribution of mean (average of the 54 sets of sample mean) RSE as Standard Error of the Mean which is Standard Deviation computed on the sampling distribution of the mean. RSE as Standard Error of the Mean approximated by population standard deviation divided by the square root of n (n=30) RSE as Standard Error of the Mean approximated by sample standard deviationofyour own sample) divided by the square root of n (n=30)(bonus points) consideration of why 6-3 and 6-4 are different. 5-aWhat is the relation between population mean and the mean of the 54 means? 5-b. Which of the two distributions (population vs sampling distribution of the means) has a narrower distribution clustered around the population mean? 5-c.To what extent, the observation of the above two (a and b) aspect of the sampling distribution lend support to the Central Limit Theorem?
Statistical Significance and Meaningfulness
For this Discussion, you will explore statistical significance and meaningfulnessReview the American Statistical Associati ...
Statistical Significance and Meaningfulness
For this Discussion, you will explore statistical significance and meaningfulnessReview 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."Post 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? 500 words or more
Be sure to support your Main Post and Response Post with reference to the week’s Learning Resources and other scholarly evidence in APA Style.
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