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Quantitative Reasoning

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MAT152 Mid-Semester Project Example

You will complete this project using the data that you collect from each of your survey participants. Each question has directions to guide you as you reflect on your project and provide answers based on the data you gathered.

Question 1: What are the questions you will be asking participants? (
Same questions approved on your discussion board.)

·
Directions: List the survey questions for your statistical study. Be specific about exactly what you will ask people. Also, record the age of each participant.
Note: These should be the same questions approved by your instructor from the discussion board.  Carry out the study. Obtain
at least 20 participants for your study.

·
Tips:

· Choose questions that interests you – something different from the examples provided.

· Avoid simple “yes” and “no” questions without an explanation.

· Have participants expand upon their answers. If they answered yes, why did they do so?

· Record the ages of your participants in a table to keep your data neat!

1.
How old are you?

2.
If full-time students were to receive a stipend*, how much should they get per month?

3.
If you were given a stipend, what would you use it for? 

*Once the tuition and fees are all paid, there are still living expenses that come along with college. This is where a stipend comes in; a scholarship organization will pay the student a flexible amount of money to pay for things like books and basic living expenses.

Question 2: Who is in your sample?

·
Directions: Describe who you asked.

I asked 20 random people I saw at our campus. Most were students in my classes but a few were faculty. It took three days for me to get enough responses.

Question 3: Who was your intended population?

·
Directions: Describe the larger group you are seeking to learn about.

My intended population was community college students in Delaware.

Question 4: Do you think your sample helps you learn about your population? What could you do (if you had more time and money) to gather a sample to better help you learn about your population?
Explain in a minimum of 2 sentences.

·
Directions: In most cases your sample is probably
not perfect. Tell what is good about your sample and how it could have been improved.

Unfortunately, no. My small sample size of 20 is not enough for my study to may inferences on the population. Additionally, a few faculty members answered the question and they were not in my intended population.

Question 5: Using your

non-numerical
(the question that did not have a number answer) data, make a pie chart or a bar graph.

·
Directions: Clearly label the information in the graph and make a descriptive title, so that it is easy for a reader to understand what is being shown. You can do this by hand or using technology. You may need to group similar responses to create a reasonable number of categories.


I noticed that several categories could be combined, so I used the 5 on the right to create by graphical display.

Question 6: Describe the information shown in the graph.

·
Directions: Summarize the data from the shown in the graph you made in question #5. Tell what percentages of respondents fit into each category and describe any interesting, surprising, or noteworthy results. Explore percentages within your data.

There were nine unique responses to the non-numerical question. I grouped up similar responses and found that the most popular spending categories would be “transportation” and “school needs”. Both of these categories were 30%, while clothes, food, and entertainment were 15%, 15%, and 10% respectively.

I was surprised because I thought more people would spend more money on entertainment. If we were to break down the categories to necessities vs luxuries, we would find that 90% of people would spend stipend money on necessities.

Question 7: Using your

numerical
data (the question with a number answer), calculate mean, median, range, and standard deviation.

·
Directions: You can do this by hand or using technology.
Show work or include the Excel spreadsheet with formulas.

Mean*

$895

Median*

$1000

Range*

$1000

Standard deviation*

$330.49

*Show work for each or include your Excel spreadsheet with formulas

Question 8: Describe the numerical results.

·
Directions: Summarize the data. What are your mean, median, range, and standard deviation? Describe these numbers in the context of your question. What does it tell you about the population? What does the standard deviation tell you about how spread out your data is? Do these numbers make sense given real world context?

It seems that most participants think around $1000 is a reasonable monthly stipend for Full-time college students. A mean of $895 being lower than the median of $1000 implies that there are a few low responses that “pull” the average down lower than what the median is. If the mean was significantly different, I would look for an outlier in my data. The range of $400-$1400 does not seem unreasonable and a standard deviation of $330 implies that most of my responses were spread between $565 and $1225. All of these numbers make sense given real world context and seem reasonable when looking at the original data collected.



Question 9: Give an overall summary of your data.

·
Directions: Write a contextualized summary about your data. Explain the graph(s) you created. In words, state what your mean and median values were and what that tells you about your population. State what percentages and ratios you found and what that tells you about your population. Use words from the course (such as majority, plurality, maximum, minimum, mean, median, …) when appropriate. What conclusions can you make? What was interesting or surprising? What additional questions would you ask in a follow-up study?

Twenty participants were asked if Full-time students were given a stipend how much should it be and what would they spend it on. Everyone seemed to give reasonable answers that ranged from $400 to $1400 per month and their spending categories varied from necessities to luxuries. The plurality of participants would spend their money on transportation or school needs. Stipend amounts averaged at $895 with a median (and mode) of $1000.

Although some students would spend money on luxury items, a large amount of participants would spend it appropriately. In a follow up study, I would want to give a stipend and track their success in the college.


Choose 2 of the 3 Questions Below to Answer:

·
Directions: Connect concepts from the semester to our project! Think critically about how you could apply topics from the semester thus far. Use specific examples to support your answers. 



Question 10: Should everyone’s responses be weighted equally?
Explain in a minimum of 2-3 sentences.

Normally I would say yes, everyone’s opinion should count equally. This study focuses on student stipend, so I should weigh the responses from the faculty less. Alternatively, it would probably make more sense to remove them from the sample.



Question 11: If you were to conduct your study again, explain how you would be able to apply the concepts of absolute and relative change.


For example, if you were to conduct this survey again in five years, what changes would you look for? Be specific to your data and variables.
Explain in a minimum of 2-3 sentences.

I could ask the same group of students a year after to see if the amount of stipend changed or what they spend money on changes. I would assume that we would get valuable information as a student experiences different classes and situations in college. They may find they need more or less money. The student may want to spend their money differently. I could calculate the amount by which the average suggested stipend changed (absolute change) and the percentage of this increase or descrease (relative change). I could also calculate the absolute and relative change of the percentage planning to spend money on a particular category.

Question 12: How could you apply the probability concepts learned in lesson 4 to your data?

Give specific numbers from your data and connect to your population.
Explain in a minimum of 2-3 sentences.

I could use the categorical data collected from my sample to make inferences about the population. For example, if 6 of my respondents would spend stipend money on school needs, I could infer that 30% (6/20) of the population of DTCC would spend their money on school needs.

Rubric Goals: Use these requirements as a guide to ensure that you complete this project to the best of your ability.

Rubric Criteria

Exemplary Top Score Requirements

Did I do this?

Question(s) is well written

(Question 1)

Question(s) is well-written and relevant. Question(s) has multiple answer options and/or requires explanation

Sample and population are explicitly described.

(Question 2 &3)

Concept of population and sample seems to be understood. 

Representative sample analysis

(Question 4)

Concept of representative samples seems to be understood. 

Graph of non-numerical data

(Question 5)

Concepts of creating a graph seem to be understood. (Graph has clear labels and a descriptive title; gives a helpful representation of your data)

Data summary from graph

(Question 6)

Concept of describing and summarizing data seems to be understood. (Data is accurately described, accurate percentages are listed, summary is clearly written)

Calculations with numerical data

(Question 7)

Calculations are accurate: All four measures are accurately calculated and work is clearly shown (or an Excel spreadsheet including formulas is included).

Data summary from calculations

(Question 8)

Concepts of describing and summarizing data seem to be understood. (Results of mean, median, range, and standard deviation are accurately reported and their meaning in this context is clearly described)

Overall summary

(Question 9)

Overall summary of data from your survey questions is well done (accurately describes the data, focuses on important and interesting points, puts results in the context of what you learned about your population)

Connections

(Question 10-12)

At least 2 concepts from the semester were accurately connected to the project. Specific details of how these concepts could apply to your data are included.

Professionalism

Project is submitted entirely on time.

Presentation and grammar

Project is neatly prepared with proper grammar.

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