Category: Statistics

Instructions
For this discussion post, we are going to construct a confidence interval for the sample mean using the Z-distribution: 
We would like to create an interval to estimate the average recovery time for patients undergoing a new ACL tear recovery program. We sampled 45 patients who underwent this new recovery program and saw the average recovery time to be 285 days. If the population standard deviation can be assumed to be 100 days, compute the 90% confidence interval for the mean recovery time. 
Discussion Prompts
Answer the following questions in your initial post: 
The Z-distribution will be used to create the confidence interval for the mean. Why are we able to use this distribution for this problem?
Create your confidence interval and report what it is. 
The current ACL recovery program averages 320 days to fully recover. Based on the confidence interval you constructed, where does this value fall?
Based on the confidence interval, do you think we have enough evidence from a statistical standpoint to say the new procedure is significantly better than the current procedure? Why or why not?
Supporting Resources: https://www.youtube.com/watch?v=DT-fPG0Hff8Links to an external site. 

Statistics Project Description
You are about to embark on an adventure which will merge the mathematics you are studying with the world around you.  Data sets will be provided and are different for each student; hence this is an individual project and assessment.  Follow the project outline below in constructing your paper.  The length will range from 5-8 pages including text, tables and graphs.  It will be typed in 12-point font, paginated, double spaced with one-inch margins.  A cover page is optional and does not count towards paper length.  Incorporate Geogebra results and graphs.  It is okay to write out any calculations and graphs by hand.  Check the rubric for grading details.
Statistics Project Outline Template
Introduction
Consider your assigned data sets.  What topics might you investigate and why? Consider comparisions among groups, aggregated data(e.g. separated by gender, location, relationship status, health condition etc.) and disaggregated data.
Research questions(at least two): What you are interested in finding out?  These questions will be answered using your assigned data sets. Examples: https://www.bl.uk/business-and-ip-centre/articles/what-are-typical-quantitative-research-questionsLinks to an external site.
Data
Source of data
Identify the variables
Describe the types of variables(qualitative or quantitative)
Give the level of measurement for each variable
Findings
Descriptive statistics
For quantitative data, provide sample sizes, means, and standard deviations
For qualitative data, provide counts, sample sizes, and p’
If relevant to your research question, disaggregate the above data by age, gender, etc.
Relevant tables, graphs, and charts(you must have at least two graphs)
Confidence Intervals(include type, statistics, conditions, confidence level, critical value, error bound, confidence interval and sentence)
Interval 1
Interval 2
And so on for each additional interval(you must have a least two intervals)
Estimate the sample size for a “nice” error bound for one of your confidence intervals
Hypothesis Tests(include type, hypotheses, significance level, statistics, conditions, standardized test statistic, p-value, p-value sketch, conclusion and sentence)
Test 1
Test 2
And so on (Use a hypothesis for each of your research questions)
Conclusion
Answer your research questions 
Discussion
Provide a brief summary of the contents of the report including a concise statement of the research questions and results
Reflection
Reflect on your conclusions
Address any possible flaws that could have biased the data 
What have you learned from this project
Provide recommendations of new questions for future research

Overview
Confidence intervals come into play when we want to create a better approximation for what the true value of a parameter is. In this module, we will discuss the confidence interval for the sample mean. Up to this point, we have created point estimates, which is what we get when we compute the sample mean. This approximation is almost surely incorrect, so we can be better suited using an interval estimate, in this case the confidence interval.  
The concept here is we buffer our prediction of the mean using a margin of error, which uses the Z distribution, as well as a level of confidence, c. Common confidence intervals we create are 80%, 90%, 95%, and 99% confidence intervals. The approach of a confidence interval is this: If we collect sample data and run this approach repeatedly, then approximately 100*(1-c) % of the confidence intervals will contain the true value of the parameter. So, if we construct 95% confidence intervals, we expect that approximately 95% of the intervals we create will contain the true value of the parameter of interest.  
The common formula we use when construction confidence intervals for the mean is this:  
𝑥
¯
±
𝐸
where E is our margin of error. This is the value that will change depending on which distribution we are using.
If we are using the Z-distribution, then 
𝐸
=
𝑍
𝑐
𝜎
𝑛
where 
𝑍
𝑐
is our critical Z value. Now we have to figure out what our critical Z values are.  
Critical Z values will never change and are as follows:   
80% confidence interval: 
𝑍
𝑐
= 1.28
90% confidence interval: 
𝑍
𝑐
= 1.645
95% confidence interval: 
𝑍
𝑐
= 1.96
99% confidence interval: 
𝑍
𝑐
= 2.576
So, let’s walk through a confidence interval calculation using the Z distribution: Suppose we have a sample of data with a mean of 50, a population standard deviation of 10, and a sample size of 64. We want to create a 95% confidence interval for this sample: 
𝐸
=
𝑍
𝑐
𝜎
𝑛
= 
1.96
⋅
10
64
= 2.45.
Lower bound: 
𝑥
¯
−
𝐸
=
50
−
2.45
=
47.55
Upper bound: 
𝑥
¯
+
𝐸
=
50
+
2.45
=
52.45
Then we write our final answer as such: (47.55, 52.45). We can then say that we are 95% confident the true value of the population mean falls between 47.55 and 52.45.  
If we have a scenario in which we are computing a confidence interval for the population proportion, we need to ensure the following conditions have been met: Each trial is independent of one another, and we have seen at least 5 successes and 5 failures (𝑛𝑝≥5  and   𝑛(1−𝑝)≥5  ). If we meet these conditions, then the distribution of the sample proportion can be approximated using the Normal distribution, and we can use the critical Z values discussed above. 
The process of constructing the confidence interval for the population proportion will be similar to that for the mean, and constructed using 
𝑝
^
±
𝐸
, where the margin of error, E, is found as: 
𝐸
=
𝑍
𝑐
𝜎
𝑛
.
So, let’s walk through an example. A survey of 500 nurses was done to see if they were satisfied with their current employer. Of these 500 nurses, 415 claimed they were satisfied. Construct a 90% confidence interval for the population proportion. 
First, we want to compute the value of 
𝑝
^
We do that by taking the number of successes, in this case a nurse being satisfied, over the total number of nurses surveyed. This gives us 
𝑝
^
=
𝑥
𝑛
=
415
500
=0.83.
Once we have this, we can identify that 
𝑞
^
=
1
−
𝑝
^
=
1
−
0.83
=
0.17
. Next, we want to verify we can use the Normal distribution by seeing at least 5 successes and 5 failures. We have definitely met this requirement as we have 415 successes and 85 failures. So now we can compute the margin of error, E, using our appropriate critical Z value. Here is the calculation: 
𝐸
=
𝑍
𝑐
𝑝
^
𝑞
^
𝑛
=
1.645
0.83
⋅
0.17
500
=
0.0276.
Lower bound: 
𝑝
^
−
𝐸
=
0.83
−
0.0276
=
0.8024
Upper bound: 
𝑝
^
+
𝐸
=
0.83
+
0.0276
=
0.8576
Then we write our final answer as such: (0.8024, 0.8576). We can then say that we are 90% confident the true value of the population proportion falls between 0.8024 and 0.8576.  
Instructions
For this discussion post, we are going to construct a confidence interval for the sample mean using the Z-distribution: 
We would like to create an interval to estimate the average recovery time for patients undergoing a new ACL tear recovery program. We sampled 45 patients who underwent this new recovery program and saw the average recovery time to be 285 days. If the population standard deviation can be assumed to be 100 days, compute the 90% confidence interval for the mean recovery time. 
Discussion Prompts
Answer the following questions in your initial post: 
The Z-distribution will be used to create the confidence interval for the mean. Why are we able to use this distribution for this problem?
Create your confidence interval and report what it is. 
The current ACL recovery program averages 320 days to fully recover. Based on the confidence interval you constructed, where does this value fall?
Based on the confidence interval, do you think we have enough evidence from a statistical standpoint to say the new procedure is significantly better than the current procedure? Why or why not?
Supporting resources: https://www.youtube.com/watch?v=DT-fPG0Hff8

In what scenarios would you choose a MANOVA over multiple regression, and vice versa? As part of your response, consider the assumptions, advantages, and limitations of each method, as well as the practical implications for research design and interpretation of results.
Have at least one APA style in-text citation and reference (peer-reviewed and/or textbook) to support your writing

Objectives
To
successfully complete this assignment, you will be expected to:
1.   
Produce a question
that can be answered with a correlation analysis and accurately explain why the
analysis is appropriate for the data and question to be answered.
2.   
For the identified
question, perform and report one correlation analysis to test relationships
using APA-compliant format.
3.   
Produce and explain an
effective chart or graph to display information about the correlation analysis.
4.   
Produce a question
that can be answered with a regression or multiple regression analysis and
accurately explain why the analysis is appropriate for the data and question to
be answered.
5.   
For the identified
question, perform and report one regression or multiple regression analysis to
test relationships using APA-compliant format.
Instructions
Using
the Food Affordability Dataset [XLSX],
develop one program question that can be answered with a correlation analysis.
Then, perform one correlation analysis (using two continuous data points) to
test relationships. Be sure to include the JASP/Excel output and report the
findings using APA-compliant format. Additionally, you should produce an
effective chart or graph to display information about the correlation analysis.
This is likely to be in the form of a scatterplot, since correlation requires
two continuous variables. To achieve maximum credit on this criterion, you must
both accurately identify, perform, and thoroughly report the program question
and statistical findings using APA-compliant format.
Next,
develop one program question that can be answered with a regression or multiple
regression analysis. Then, perform one regression or multiple regression
analysis. Be sure to include the JASP/Excel output and report the findings of
your regression or multiple regression analysis using APA-compliant format. To
achieve maximum credit on this criterion, you must both accurately identify,
perform, and thoroughly report the program question and statistical regression
or multiple regression findings using APA-compliant format.
Once
you have gathered this information, submit a final Word document that includes
a header for each required component of this assignment. 3-4 pages not including title page and reference page. Use these provided
headers (in APA-compliant format) for each section:
1.   
Correlation Analysis.
1.   
Program Question.
2.   
Explanation of
Appropriateness.
3.   
Statistical Analysis.
4.   
Interpretation and
Report.
5.   
Chart or Graph.
2.   
Regression or Multiple
Regression Analysis.
1.   
Program Question.
2.   
Explanation of
Appropriateness.
3.   
Statistical Analysis.
4.   
Interpretation and
Report.

bio statistics questions to answer using a statistical software eg spss using a csv file of data given to answer the questions

Complete one of your own Goodness-of-Fit Test or Test of Independence from the options in this linked document below. You will use our class data to inform your hypothesis test. Model your work after the sample assignments we did in the video quizzes above. Turn in your completed Goodness-of-Fit Test or Test of Independence using the submission button below for grading. 
Choose Your Own: Goodness-of-Fit Test or Test of Independence to complete https://docs.google.com/document/d/1VUlx4UzI2by0tAzd57ZfJtFm4YtBOqJxf5_YuT92wtc/edit
Chapter 11 Project Rubric
Chapter 11 Project Rubric
Criteria Ratings Pts
This criterion is linked to a Learning OutcomeTable of Observed Values
Organized frequency table of contingency table of observed values.
1 pts
Full Marks
0 pts
No Marks
1 pts
This criterion is linked to a Learning OutcomeTable of Expected values
Organized frequency table or contingency table of expected values.
1 pts
Full Marks
0 pts
No Marks
1 pts
This criterion is linked to a Learning OutcomeHypothesis (written in the context of the claim)
H0: Good Fit OR Independence
H1: Not a Good Fit OR Dependence
2 pts
Full Marks
0 pts
No Marks
2 pts
This criterion is linked to a Learning OutcomeTest Statistic
1 pts
Full Marks
0 pts
No Marks
1 pts
This criterion is linked to a Learning OutcomeP-value
1 pts
Full Marks
0 pts
No Marks
1 pts
This criterion is linked to a Learning OutcomeConclusion
Accurate picture of distribution with shaded p-value. Correct decision to reject or fail to reject H0 based on the p-value and the significance level.
2 pts
Full Marks
0 pts
No Marks
2 pts
This criterion is linked to a Learning OutcomeInterpretation
Worded interpretation to “support” or “not support” in the context of the claim supported by conclusion.
2 pts
Full Marks
0 pts
No Marks
2 pts
This criterion is linked to a Learning OutcomePresenatation
Careful and thoughtful attention was given to the presentation of your project
4 to >2.0 pts
Full Marks
The project is neat and free or errors such as typos, scratch marks or egregious grammatical errors. The project is coherent and simple to follow your thought process. Correct notation and imagery is used. If the assignment is hand written, it should be legible and written on clean paper and photographed or scanned legibly.
2 to >0.0 pts
Partial Credit
The project is fairly neat and free of major errors. Typos, scratch marks and grammatical errors are few. The project is mostly coherent and simple to follow your thought process. Correct notation and imagery is used. If the assignment is hand written, it is mostly legible and is scanned or photographed so it is legible.
0 pts
No Marks
4 pts
Total Points: 14

1.Enter your data into SPSS, run frequency tables, appropriate charts, measures of central tendency and measures of variability, please attach your syntax and output.
2. Formulate and test the hypothesis in which:
Please use 5 steps hypothesis testing model and be as detailed as possible in your calculations and explanations.

Chapter 12 Project
Linear Correlation and Regression Project 
Collect data for two variables. Collect at least 15 pairs of such data. Be sure the data follows the necessary requirements presented in chapter 12.
State your hypothesis/claim in words so I know what two variables, x and y,  you are analyzing. 
Clearly organize your data in a table and graph it as a scatter plot on a set of axes.
Find the linear correlation coefficient r  and state what its value suggests about the relationship between x and y.
Test to see if there is a linear correlation between the variables x and y by finding the P-value. Include the hypotheses, how the p-value determined the conclusion of the hypothesis test and a written interpretation of that conclusion in the context of the claim (hypotheses). Use a 0.05 significance level.
Find the regression equation and accurately draw and label it on your scatter plot.
Use the regression equation to make a prediction about the population your data came from. Do this even if your hypothesis test says no correlation exists.  For example, if a father’s height is 83” what is the predicted height of his son? 
Variable Examples (but please feel free to get creative – use our class data, or try using data analytics from your phone or smartwatch or social media accounts)
The heights of a father and son
The number of square feet in a house and the number of people living in that house
The number of hours people spend exercising each week and their resting heart rate
Number of miles on an odometer and the mean number of hours driven per day
Number of hours on your phone each day and the number of apps on your phone
NFL team wins this season and total number of points scored this season
People’s typing speed and texting speed
Student’s reaction time and typing speed 
If you don’t want to use our class data, you can collect your own, just be sure to collect at least 15 pairs. Here are a few links to some other data sets that would work if you are interested in these topics: 
Global Average Temperatures AnomaliesLinks to an external site.
Arctic Ice DataLinks to an external site.
World Grain Consumption DataLinks to an external site.
Hourly Wage by Race and GenderLinks to an external site.
Upload your completed assignment as a single pdf using the “submit” link below.
There is no sample assignment for this project. At this point in the semester you are well skilled at producing a complete hypothesis test and all its necessary requirements. Please only submit your neatest and best work. Sloppy and illegible work will not be graded. Please proofread your assignment for errors before you submit it. Check out the attached rubric for more grading specifications. 
Chapter 12 Paper Assignment
Chapter 12 Paper Assignment
Criteria Ratings Pts
This criterion is linked to a Learning OutcomeClaim
Present your claim in words of linear correlation for the defined population and paired quantitative data.
2 to >0.0 pts
Full Marks
0 pts
No Marks
2 pts
This criterion is linked to a Learning OutcomeData
Organized data (at least 15 pairs) in a table and graphed in a scatter plot
2 to >0.0 pts
Full Marks
0 pts
No Marks
2 pts
This criterion is linked to a Learning OutcomeCorrelation Coefficient r
State its value and what it suggests about the relationship between x and y
3 to >0.0 pts
Full Marks
0 pts
No Marks
3 pts
This criterion is linked to a Learning OutcomeHypothesis Test
Test to see if there is a linear correlation between the variables x and y by finding the P-value. Include hypothesis written symbolically and in words. Indicate how the p-value determined the conclusion of the hypothesis test and a written interpretation of that conclusion in the context of the claim (hypotheses). Use a 0.05 significance level. Include how the results of the hypothesis affect the use of the regression equation.
3 to >0.0 pts
Full Marks
0 pts
No Marks
3 pts
This criterion is linked to a Learning OutcomeRegression Equation
Find the regression equation and accurately draw and label it on your scatter plot.
2 to >0.0 pts
Full Marks
0 pts
No Marks
2 pts
This criterion is linked to a Learning OutcomePrediction
Use the regression equation to make a prediction about the population your data came from. Do this even if your hypothesis test says no correlation exists.
3 to >0.0 pts
Full Marks
0 pts
No Marks
3 pts
This criterion is linked to a Learning OutcomePresenation
Careful and thoughtful attention was given to the presentation of your project
4 to >2.0 pts
Full Marks
The project is neat and free or errors such as typos, scratch marks or egregious grammatical errors. The project is coherent and simple to follow your thought process. Correct notation and imagery is used. If the assignment is hand written, it should be legible and written on clean paper and photographed or scanned legibly.
2 to >0.0 pts
Partial Credit
The project is fairly neat and free of major errors. Typos, scratch marks and grammatical errors are few. The project is mostly coherent and simple to follow your thought process. Correct notation and imagery is used. If the assignment is hand written, it is mostly legible and is scanned or photographed so it is legible.
0 pts
No Marks
4 pts
Total Points: 19

Formulate and test the hypothesis in which:
Please use 5 steps hypothesis testing model and be as detailed as possible in your calculations and explanations
I will provide the PDF with it