Category: Statistics

MAT141 Assignment 1 Spring 2026 Descriptive Statistics and Making Graphs Basic Instructions This assignment is worth 5% of your final grade. Assignments must be uploaded as Word documents to TurnItIn via Classes, by the end of the day on Wednesday, Feb 18. In case you run in to technical difficulties, plan to submit it EARLY. See your instructor during her office hours or via Zoom appointment (Mon & Wed 4:30-6:00pm, Thu 3:00-5:00pm virtual) , Password: 123456), if you have any questions about the assignment. Make sure you submit your assignment in ONE file (either pdf or word), which includes the actual write-up for the assignment, both graphs you produced, and screenshot of your csv data file and screenshot of the R script that you used to complete your assignment. You could also use R markdown to complete your assignment. Assignment Objectives The goal of this assignment is to describe a sample, to estimate parameters of a population using the sample, and to visualize the data using graphs (histogram and boxplot). You will need to find or collect sampled data on your own. The data must be numerical, and must be a single variable (i.e., not comparing two groups). You could get the data from a book, from a website, or from an experiment you conducted yourself. Each student in the class must have her/his own data no data sharing! Your instructor recommends NOT using time as the unit of replication (i.e., each data point should not specifically be from a different time period it should be from a different individual person/animal/tree or place place including a hospital, petri dish, soil specimen, etc.). Remember too, that if you are estimating the frequency of occurrence in different places, it is typically more appropriate to convert these values to proportions (e.g., the proportion of people at each hospital that caught the flu, instead of the number of people at each hospital that caught the flu. This will control for the fact that there are a different number of people admitted to each hospital.) You are to do all calculations in R, and also create the graphs using R. Save your graphs and open them in a Word document, or copy and paste graphs into a Word document that also contains your written answers. Avoid using screen shots. Plagiarized work will results in a grade of ZERO for the entire assignment. Plagiarizing content on more than one assignment will result in an F in the course. Assignment Components Title: A short (one sentence) description of your study. (1 point) Introduction: Explain the goal of your study. What is the purpose of conducting the study? (1 point) What population are you trying to describe using a sample? (e.g., is it a population of hospitals in NYC?) (1 point) Methods: Describe, in words, how the sample data were collected from a population, including the sample size and the units (1 point). Explain what descriptive and inferential statistics you will use to describe the sample (Chapters 3 and 4 of your textbook) and state that you will use R calculate these statistics (1 point). Results: Write one sentence briefly describing your results, and include units in this sentence. In a table, present the mean, median, upper and lower quartiles, standard deviation, standard error, and approximate 95% confidence interval (5 points). Present a frequency histogram displaying the data (4 points). Present a boxplot displaying the data (4 points). ALWAYS label figure axes properly. ALWAYS include figure captions (at the bottom of the figure) describing what the figure represents, including the sample size in the caption. ALWAYS include table captions (at the top of the table) describing what the table represents, including the sample size in the caption. ALWAYS include units in figures and tables (captions, axes, column headers). Failure to do any of the above bullet-point steps will result in deducted points. Discussion: State your conclusion about the population, based on your statistics (and specifically based on your 95% confidence interval) (1 point). Referring back to the classes on sampling methods, do you think that you accurately and precisely estimated the mean of the population, or do you think there was bias or sampling error? (0.5 points for discussing bias and 0.5 points for discussing sampling error) HINT! Remember that if you repeated the experiment many times, you expect your sample mean to fall within the 95% confidence interval 95% of the time. Example notes and feedback to previous students: You should mention the version of R and R-studio softwares you used. For example: “R-studio Version 2024.12.0+467 (2024.12.0+467) was used to analyze the statistics”. I don’t see your raw data and r script, so I can’t tell whether you reported the correct numbers. Standard deviation of mean is one of the inferential statistics. What descriptive and inferential statistics did you use to describe the sample?

In this assignment, you will read the article (attached below) in preparation for your final project. This article has a similar topic to your final, so take your time and read it well. You will be summarizing the article using the MEAL plan and recording a video reflection of what you learned about the statistical applications within this article that you will be using in your final project.

M-main idea of the article

E-evidence that you have identified the main idea use at least three citations from the article itself in APA format

A-analysis of the article–what does it mean to your future career did it add any value to what you already understood?

L-link–how does this article connect to you personally within your Christian worldview especially in light of the fact you final project will be using many of the techniques with the article?

For the video section of this assignment please create a casual script that is to be used to read for the video that includes:

–A reflection based on your MEAL plan and your personal feelings about the statistical applications you will be applying soon in your final project.

video link: https://youtu.be/m0GQv4ub-_0

In this assignment, you will complete the calculation of Pearson (r) for each data set pair. You will also provide the steps you used to produce this solution as well as define each mathematical symbol translating it into words. This work must be done with all necessary calculations.

X 1 = x={9,10,11,12,21} y= {2,5, 23,4,19}

X 2 = x={5,9,13,61,2} y= {9, 32, 5,6,15, 18}

X 3 = x={24,19,13,8,2} y= {28, 5, 9,6,25, 8}

Please also provide: central tendency, variance, and range for each dataset.

ANSWER ALL OF THE QUESTIONS FROM THE ATTACHMENTS (i.E., SCREENSHOTS AND PROBABILITY LAB) AND PROVIDE STEP-BY-STEP INSTRUCTION AND EXPLANATION ON HOW YOU GOT YOUR ANSWER. PLEASE ENSURE YOU SHOW YOUR WORK, PLEASE USE ITHENTICATE/TURNITTIN AND AI REPORT.

ANSWER ALL OF THE QUESTIONS FROM THE ATTACHMENTS (i.E., SCREENSHOTS AND PROBABILITY LAB) AND PROVIDE STEP-BY-STEP INSTRUCTION AND EXPLANATION ON HOW YOU GOT YOUR ANSWER. PLEASE ENSURE YOU SHOW YOUR WORK, PLEASE USE ITHENTICATE/TURNITTIN AND AI REPORT.

Below are 4 of peers discussion post. with a minimum of 150 words create a response that is casual and conversational. please answer each seperately.

Discussion Post 1 Peer Post 1: (AB)

The Question and the Variables

My question is “Am I a responsible student?” My variables are number of hours I spend studying per week and how many classes I miss in a semester. I think that these are two of the major aspects of being a responsible student, so they are very useful in understanding whether or not I am one.

The Participants

My participants are my parents, my Aunt and Uncle (who are essentially my parents while I am out of state at school), and my grandma. I was struggling to find a sixth invested adult with an official title who was available to partake, so I utilized an accountability partner. My accountability partner I will be using for this study is Gianna, who is an older teammate who keeps me accountable in my Bible reading. I believe that all six of these adults are very invested in my life and know me very well.

Determine how they measure movement in the data.

There is not much movement in this data. The numbers in both sets do not vary too far from each other, and are relatively consistent. My grandma mentioned that she thinks I would study more if I were less busy with dance. This implies that she thinks my number of study hours would increase in weeks with less or no dance. Several people also mentioned that I would not miss class for unexcused reasons, unless I were sick. This implies that the number of classes I miss would rise at the occurrence of any of these events.

Identification of Variables

Mom: I would say my mom’s comments and data reflect my motivation. She mentioned that knowing what I am doing matters to me, and that shows motivation as to why I would not miss class and spend many hours studying.

Dad: My Dad’s comments and data reflect my attitude about life. He stated that I am dedicated, which is a reflection of how I react in life.

Uncle: My Uncle’s comments and data reflect my motivation. He stated that my parents would not be happy if I missed class, which is a major motivator to attend.

Aunt: My Aunt’s comments and data reflect my attitude about life. Specifically, this is shown in her stating that I am dedicated and that I would feel guilty missing a day of classes.

Grandma: My grandma’s comments and data reflect my attitude about life. This shows in her comments about my perfectionism and responsibility. I also found it very interesting how she answered my original question without ever being asked it when she stated that I am responsible.

Accountability partner: Gianna’s comments and data reflect my motivation. She stated that I am hard-working, which shows some sort of underlying motivation.

Psychological Hypothesis

The data from the invested adults in my life see my responsibility as a student through the lenses of motivation and my attitude about life.

Discussion Post 1 Peer Post 2: (RW)

Question:

How do invested adults use data about my academic behavior to evaluate my growth?

Participants:

Professor, Coach, Parent, Counselor, Pastor, Accountability Partner (6 total)

Variables (15 scale):

• Academic consistency
• Perceived growth over time
• Confidence in my future success

Use of Data:

Adults use grades, effort, attitude, and behavior patterns.

Movement is measured by improvement over time.

Data Table

Role

Consistency

Growth

Confidence

Mindset

Professor

4

4

5

Belief in Self

Coach

5

4

4

Motivation

Parent

4

5

5

Attitude

Counselor

3

4

4

Things to Do

Pastor

4

3

4

God-Given Ability

Accountability Partner

3

4

4

Things to Do

Psychological Hypothesis:

Invested adults primarily frame my growth through effort and consistency, showing a mindset focused on development over time.

Discussion Post 2 Peer Post 1: (KL)

Hypotheses

Research Question:

How do invested adults evaluate my development as a volleyball player and team leader?

Because you collected ratings (110) on three variables, the cleanest inferential focus is whether the mean ratings are significantly high (above an acceptable benchmark, commonly 7 = above average).

Variable 1: Technical Skills

• Null Hypothesis (H0): t 7
• Alternative Hypothesis (H1): > 7

Variable 2: Leadership

• Null Hypothesis (H0): d 7
• Alternative Hypothesis (H1): d > 7

Variable 3: Mental Game

• Null Hypothesis (H0): m 7
• Alternative Hypothesis (H1): m > 7

(This aligns with a one-sample mean comparison, appropriate for your small n = 6.)

Raw Data:

8, 9, 9, 9, 9, 8.5

StatisticValueMean (x)8.75Median9Mode9Range1Variance (s2)0.17Standard Deviation (s)0.41

Frequency & Relative Frequency

ScoreFrequencyRelative Frequency8.0116.7%8.5116.7%9.0466.6%Table 2. Leadership (110)

Raw Data:

8, 9, 9, 9, 8, 7

StatisticValueMean (x)8.33Median8.5Mode9Range2Variance (s2)0.56Standard Deviation (s)0.75

Frequency & Relative Frequency

ScoreFrequencyRelative Frequency7116.7%8233.3%9350.0%Table 3. Mental Game (110)

Raw Data:

10, 7.5, 8, 8, 7, 8

StatisticValueMean (x)8.08Median8Mode8Range3Variance (s2)0.92Standard Deviation (s)0.96

Frequency & Relative Frequency

ScoreFrequencyRelative Frequency7.0116.7%7.5116.7%8.0350.0%10.0116.7%3. Graphing the Analysis (Descriptive + Inferential)

see attachment below

Figure 1 displays the mean ratings for technical skills, leadership, and mental game, with standard deviation error bars. All three mean scores exceed the benchmark value of 7 used in the hypothesis testing. While variability is greatest for mental game, the mean ratings for all variables remain above the reference line, providing visual support for the rejection of the null hypotheses.

M Main Idea

The results of this mini-study indicate that invested adults perceive my technical skills, leadership, and mental game as significantly above average, supporting the alternative hypotheses for all three variables.

E Evidence

The mean ratings were 8.75 for technical skills, 8.33 for leadership, and 8.08 for mental game, all exceeding the benchmark score of 7. Frequency distributions showed that most responses clustered at 8 and 9, indicating consistency across evaluators. Qualitative feedback further reinforced these findings by highlighting court awareness, communication, accountability, and resilience.

A Analysis

These results suggest that my strengths lie not only in physical performance but also in leadership and psychological resiliencekey traits for collegiate athletics and future professional environments such as healthcare. The slightly higher variability in mental game scores indicates an area for continued growth, particularly in emotional consistency under pressure, which is critical for both athletic performance and patient-centered careers.

L Link to Christian Worldview

From a Christian worldview, this data reflects the biblical principle of stewardshipusing God-given talents responsibly while remaining open to growth (Colossians 3:23). Data analysis allows me to evaluate my abilities honestly, remain humble in strengths, and intentionally improve weaknesses, aligning personal development with faith-based accountability and service to others.

Discussion Post 2 Peer Post 2: (TC)

Because this mini-study looks at whether invested adults observe positive growth in you over time, the clearest inferential focus is on the Growth Trend variable.

• Null Hypothesis (H0):
• H_0: mu_{growth} = 0
• (There is no overall growth trend observed by invested adults.)
• Alternative Hypothesis (H1):
• H_1: mu_{growth} > 0
• (Invested adults observe a positive growth trend.)

3. Graphical Analysis (Descriptive + Inferential)

• Descriptive statistics:
• Bar charts were used for all three variables to clearly show distribution patterns across invested adults. These graphs show clustering at higher values (45 for consistency and follow-through, +1 for growth).
• Inferential reasoning:
• The Growth Trend mean (0.83) is well above the null value of 0, and 83.3% of participants reported positive growth, which provides support for rejecting the null hypothesis in favor of the alternative.

(You already saw the graphs generated those are exactly what your professor wants.)

4. MEAL Narrative (Ready to Submit)

M Main Idea

The purpose of this analysis was to examine how adults who are invested in my life use observable data to evaluate my consistency, follow-through, and overall growth trend over time.

E Evidence

Descriptive statistics showed high average scores for both consistency (M = 4.17) and follow-through (M = 4.00). Most notably, the growth trend variable had a mean of 0.83, with 83.3% of invested adults reporting positive growth. Low variance and standard deviation values indicate strong agreement among participants.

A Analysis

These results suggest that multiple invested adults independently observe similar patterns of discipline, accountability, and improvement in my behavior. This is meaningful for my future career because learning to track performance data, interpret feedback, and demonstrate measurable growth is essential in psychology, leadership, and professional development.

L Link (Christian Worldview)

From a Christian worldview, this data reflects the biblical principle of growth through accountability and stewardship. Proverbs 27:17 teaches that iron sharpens iron, and this study shows how God uses invested relationships to refine character. Using data honestly and responsibly allows me to pursue excellence while remaining humble and teachable in both faith and vocation.

To become proficient in statistical reasoning, you need to be able to interpret data from surveys. This includes preparing frequency tables and graphs, as well as histograms.

Imagine you are an intern with a community clinic. Your organization conducted a survey regarding patient satisfaction. Your supervisor has given you the original survey and the and asked you to prepare a summary including the following:

• Frequency Table
• Frequency Bar Graph
• Histogram
• A 250-word written summary describing the trends and/or patterns observed in the frequency table, frequency bar graph, and histogram.

Please include your name on your Wk 1 – Survey Results Summary: Frequency and Histogram paper.

Submit your assignment as a Microsoft Word document.

Resources

PLEASE INCORPORATE INFORMATION FROM CHAPTER 1-2 from this textbook

Statistics for Psychology, 7th edition

Published by Pearson (July 1, 2022) 2023

Arthur Aron State University of New York at Stony BrookElliot J. Coups Robert Wood Johnson Medical School, Rutgers State University of New JerseyElaine N. Aron State University of New York at Stony BrookErin Cooley Colgate University

Aron, A., Coups, E. J., Aron, E. N., & Cooley, E. (2023). Statistics for psychology (7th ed.).

instruction are on attachment