Fall 2023 Capstone Project
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School
East Tennessee State University *
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Course
MISC
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
23
Uploaded by BaronRockSeaUrchin35
Fall 2023 Capstone Project (100 points)
Due: Friday, December 8 by 5 pm in D2L’s drop box
A total of 702 students responded to the MATH-1530 class survey. Here are some of the questions that were asked on the survey: 1.
Classification - What is your classification in college? (Freshman/First Year, Sophomore, Junior, Senior, Graduate Student, Dual Enrollment, Other) 2.
Film - Which of the following describes your favorite genre of film? (Action, Children, Comedy, Drama, Horror, Romance, Sci-Fi, Other) 3.
Salary - What is your ideal starting salary (yearly, not hourly, that you wish to make after graduating from college? 4.
Shoe-Size - What is your Shoe Size? 5.
Age - What is your Age in years? 6.
Height - What is your Height in inches? 7.
Weight - What is your Weight in pounds? 8.
Exercise - How often do you exercise? (Never, Almost Never, Sometimes, Fairly Often, Very Often) 9.
Political-Party - With which political party do you identify? (Democrat, Independent, Republican, No Political Affiliation, Other) 10.
Vote - How likely are you to vote in the next presidential election? (Not Likely, Likely, Very Likely) 11.
Consider - If you are Likely or Very Likely to vote in the next presidential election, would you consider voting for a minority party candidate in the upcoming election? That is, would you be willing to consider a Third-Party candidate? (Would Consider, Would Not Consider) 12.
DoomScrolling - Doomscrolling is the act of spending an excessive amount of screen time devoted to the absorption of negative news. How often do you find yourself engaging in doomscrolling? (Never, Rarely, Sometimes, Very Often) 13.
Time_DoomScrolling - If you responded to anything other than "Never" to the prior question, you were asked. In a typical day, how many
minutes do you feel that you spend on an electronic device such as your phone, tablet, or computer Doomscrolling? 14.
Firearms - In general, do you feel that the laws covering the sale of firearms should be made more strict, less strict, or kept as they are now? (More Strict, Less Strict, Kept as they are now) 15.
Constitution - Would you prefer to amend the Constitution so the candidate who receives the most total votes nationwide wins the election, or to keep the current system, in which the candidate who wins the most votes in the Electoral College wins the election? (Amend the Constitution, Keep the Current System) Two additional variables were created from the data. 1.
Age-Group - This variable is classifying an individual based on their age as either: Less than 20, 20-29, 30-39, 40-49, 50 or over. 2.
BMI - Body Mass Index
You must use Minitab to analyze the data for this project. The data file is in D2L at our course homepage and is called Fall 2023 Capstone Data
.
1.
The survey contains a number of variables. Identify the following as Categorical or Quantitative
variables. Salary –
Quantitative Film –
Categorical Age-Group –
Categorical Age –
Quantitative Classification –
Categorical
BMI Body Mass Index is seen on various health forms. The Math 1530 class survey asked "What is your height in inches?" and "What is your weight in pounds?". Using this information, we calculated BMI and stored the information inside the Minitab file. Use this information to answer the following questions: 2.
Create an appropriate graph to display the distribution of BMI and insert it here. FALL 2023 CAPSTONE DATA.MWX Histogram of BMI 3.
Which of the following best describes the shape
of this distribution? Highlight your answer: Strongly Skewed Right, Strongly Skewed Left, Fairly Symmetric, Uniform, or Bimodal
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4.
Create summary statistics
for the variable BMI
and insert them here: FALL 2023 CAPSTONE DATA.MWX Descriptive Statistics: BMI Statistics Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum BMI 686 16 25.819 0.243 6.365 15.619 21.255 24.211 28.763 55.734 5.
Which statistics are appropriate to describe the Center
and Spread
of the BMI
variable? Due to outliers, use the Median for center and the Quartiles for spread. The median BMI is 24.211 and Q1=21.55 and Q3=28.763 6.
Create a graph to show any outliers
for the BMI
variable: FALL 2023 CAPSTONE DATA.MWX Boxplot of BMI 7.
Calculate the summary statistics of BMI
classified by Age-Group
and insert the Minitab output here:
FALL 2023 CAPSTONE DATA.MWX Descriptive Statistics: BMI Statistics Variable Age-Group N N* Mean SE Mean StDev Minimum Q1 Median Q3 BMI 20-29 163 4 27.100 0.510 6.516 16.242 22.312 25.745 30.894 30-39 25 0 33.37 1.51 7.57 23.91 27.84 31.32 37.27 40-49 9 0 31.95 1.88 5.64 24.96 27.39 30.34 37.21 50 or over 8 0 28.75 1.46 4.14 20.60 26.44 29.67 31.87 less than 20 481 12 24.828 0.268 5.873 15.619 20.672 23.616 27.445 Variable Age-Group Maximum BMI 20-29 51.366 30-39 51.68 40-49 41.19 50 or over 33.44 less than 20 55.734 8.
What is the average BMI for the “50 or over” Age
-Group? 28.75 What is the standard deviation of BMI for the “30
-
39” Age
-Group? 7.57 What is the maximum value
of BMI for the “less than 20” Age
-Group? 55.734 What is the first quartile
of BMI for the “40
-
49” Age
-Group? 27.39 9.
Give a graphical comparison of BMI separated by Age-Group
. Insert the Minitab graph here: FALL 2023 CAPSTONE DATA.MWX Boxplot of BMI
10.
Which age group has the largest maximum
value? “less than 20”
Which age group has the most outliers
? “less than 20”
Which age group has the smallest IQR
? “50 or over”
11.
Give a brief description of BMI
as it compares
to the different Age-
Groups
: The lowest Median BMI is in the “less than 20” age
-group, and this group has the most outliers. The distribution of BMIs in the “30
-
39” and “40
-
49” age
-groups are very similar
. BMIs in the “50 or over” age
-group have the least amount of variability.
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Favorite Genre of Film The Math 1530 Fall 2023 survey asked, "Which of the following describes your favorite genre of film?" Use this information to answer the following questions. 12. Create an appropriate graph to display the distribution of the variable Film
and insert your graph here: FALL 2023 CAPSTONE DATA.MWX Chart of Film FALL 2023 CAPSTONE DATA.MWX Tally for Discrete Variables: Film Tally Film Count Action 138 Children 12 Comedy 189 Drama 46 Horror 116 Other 36 Romance 116 Sci-Fi 49 N= 702
13. If a student is chosen at random, what is the probability the student said “
Horror
”?
116/702 = 0.17 = 17% If a student is chosen at random, what is the probability the student said “
Comedy
”?
189/702 = 0.27 = 27% If a student is chosen at random, what is the probability the student said “
Action
”?
138/702 = 0.20 = 20% 14. Based on the graph, what can you conclude about the distribution of Film
? The majority of our students said they liked Comedy and the least number of students said Children’s films.
Political Party Affiliation and Considering Voting for a Third-Party Candidate The Math 1530 Fall 2023 survey asked students, "With which political party do you identify?" and "How likely are you to vote in the next presidential election?". Of the respondents that chose "Likely" or "Very Likely" to the question of likelihood of voting in the next election, we asked " Would you consider voting for a minority party candidate in the upcoming election? That is, would you be willing to consider a Third- Party candidate?"
15. Create a graph to display the relationship between Political-Party
and Consider
. Insert your graph here: FALL 2023 CAPSTONE DATA.MWX Chart of Political_Party 16. Create an appropriate two-way table to show the relationship between Political-Party
and Consider
. Be sure to remove any “missing values” under the Options setting. Insert the table here: FALL 2023 CAPSTONE DATA.MWX Tabulated Statistics: Political_Party, Consider Rows: Political_Party Columns: Consider Would Consider Would Not Consider All Democrat 76 22 98 Independent 59 16 75 No Political Affiliation 101 23 124 Other 25 2 27 Republican 129 91 220 All 390 154 544
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Cell Contents Count Probabilities from Two Way Table Suppose we select one student at random.
Calculate the following probabilities and show your work: 17.
What is the probability the selected student is a Democrat and Would Not Consider
voting for a third-party candidate? 22/544 = 0.04 = 4% 18. Given the student is a Republican
, what is the probability they Would Consider
voting for a third-party candidate? 129/220 = 0.59 = 59% 19. Given the student is a Democrat
, what is the probability they Would Consider
voting for a third-party candidate? 76/98 = 0.78 = 78% 20. What is the probability a randomly selected student is a Democrat
who Would Consider
voting for a third-party candidate? 76/544 = 0.14 = 14% 21. What is the probability a randomly selected student said they Would Consider
voting for a third-party candidate? 390/544 = 0.72 = 72% 22. What is the probability a randomly selected student is a Republican
? 220/544 = 0.40 = 40% 23. What is the probability a randomly selected student said they were a Democrat or a Republican
? (98+220)/544 = 0.58 = 58% 24. Do you think there may be an association between Political-Party
and Consider
? Conduct the appropriate Chi-Square Test to see if we have statistical evidence and insert the Minitab output here: Use Alpha = 5% or α
= .05 H
0
: There is NO
relationship between Political-Party and Consideration for a third party canidate.
H
A
: There IS
a relationship between Political-Party and Consideration for a third party canidate. FALL 2023 CAPSTONE DATA.MWX Chi-Square Test for Association: Political_Party, Consider Rows: Political_Party Columns: Consider Would Consider Would Not Consider Missing All Democrat 76 22 20 98 70.26 27.74 0.469 1.189 Independent 59 16 20 75 53.77 21.23 0.509 1.289 No Political Affiliation 101 23 87 124 88.90 35.10 1.648 4.173 Other 25 2 11 27 19.36 7.64 1.645 4.167 Republican 129 91 20 220 157.72 62.28 5.230 13.245 All 390 154 * 544 Cell Contents Count Expected count Contribution to Chi-square Chi-Square Test Chi-Square DF P-Value Pearson 33.564 4 0.000 Likelihood Ratio 34.564 4 0.000 25. What is the value of the Test Statistic? 33.564 What is the P-value? 0
26. Interpret the results of your Chi-Square Test: Since the P-value of 0 is less than alpha of 0.5, we REJECT the H
A
indicating that there IS a relationship between Political-Party and Consideration for voting for a 3
rd
party candidate. The largest contribution to the Chi-Square statistic is 13.245 which are the Republicans who say they would NOT consider voting for a 3
rd
party candidate. This is where the strongest association between these variables is located. Firearms The Math 1530 Fall 2023 survey asked, "In general, do you feel that the laws covering the sale of firearms should be more strict, less strict, or kept as they are now?" In an article from the Los Angeles Times
published on September 13, 2023, by Katherine Schaffer entitled "Key facts about Americans and guns" the article claims that "
About six-in-ten U.S. adults favor stricter gun laws
." 27. Create a tally of the variable Firearms
and insert your tally here: Tally
Firearms
Count
Kept as they are now
239
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Less Strict
53
More Strict
407
N=
699
*=
3
28. Do we have evidence to suggest that the proportion of ETSU students that favor “More Strict” gun laws is lower
than what was claimed in the article? You will need to conduct a Test of Hypothesis to test this claim. Write the correct Null and Alternative Hypotheses: H
0
: P=60% or P=.60 H
A
: P<60% or P<.60 29.
Run the Hypothesis Test using a significance level of 5% or α
= .05 and insert the correct Minitab output here: FALL 2023 CAPSTONE DATA (3).MWX
Test and CI for One Proportion
Method
p: event proportion
Normal approximation method is used for this analysis.
Descriptive Statistics
N
Event
Sample p
95% Upper Bound
for p
699
407
0.582260
0.612944
Test
Null hypothesis
H₀: p = 0.6
Alternative hypothesis
H₁: p < 0.6
Z-Value
P-Value -0.96
0.169
30. What is the value of the Test Statistic? Z=-.96 31. What is the P-value? 0.169 32. What is your Conclusion of this hypothesis test? Since the P-value of .169 is not less than alpha of .05 we KEEP the null hypothesis. We do NOT have enough evidence to say that the proportion of ETSU students who favor more strict gun laws is lower than 60% Do our results seem to support or contradict the article that says “
about 6 in 10 U.S. adults favor stricter gun laws”?
Explain: Our results support this article. The article says about 60% of US adults favor stricter gun laws and in our sample about 58% said they felt gun laws should be stricter. This is very close to the 60% parameter mentioned in the article 33. Use Minitab to find a 95% confidence interval for the proportion of ETSU students who favor stricter gun laws? FALL 2023 CAPSTONE DATA (3).MWX
Test and CI for One Proportion
Method
p: event proportion
Normal approximation method is used for this analysis.
Descriptive Statistics
N
Event
Sample p
95% CI for p
699
407
0.582260
(0.545699, 0.618822)
34. Interpret the 95% confidence interval: We are 95% confident that the true proportion of ALL ETSU students who favor stricter gun laws lies between 54.6% and 61.9% Comparing the proportion of Democrats to Republicans that would consider voting for a Third-Party candidate. An article from NBC news entitled "More Democrats than Republicans are open to a third-party candidate" was published on June 28, 2023 by Ben Kamisar. We are interested in knowing whether a larger proportion of Democrats or whether a larger proportion of Republicans from the
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student body at ETSU are considering voting for a third-party candidate. FALL 2023 CAPSTONE DATA (3).MWX
Tabulated Statistics: Political_Party, Consider
Rows: Political_Party Columns: Consider
Would
Consider
Would Not
Consider
All
Democrat
76
22
98
Independent
59
16
75
No Political Affiliation
101
23
124
Other
25
2
27
Republican
129
91
220
All
390
154
544
Cell Contents
Count
35
.
How many students in our sample said they were Democrat?
98 Of the students who said they were Democrat, how many of them said “they would consider voting for a third-
party candidate?”
76 or 76/98 How many students in our sample said they were Republican? 220 Of the students who said they were Republican, how many of them said “they would consider voting for a third-
party candidate?”
129 or 129/220
36. Again, we are interested in knowing whether a larger proportion of Democrats or a larger proportion of Republicans from ALL students at ETSU would consider voting for a third-party candidate. Run the appropriate statistical test in Minitab using a significance level of Alpha = 5%. Paste your output here: FALL 2023 CAPSTONE DATA (3).MWX
Test and CI for Two Proportions
Method
p₁: proportion where Sample 1 = Event
p₂: proportion where Sample 2 = Event
Difference: p₁ - p₂
Descriptive Statistics
Sample
N
Event
Sample p
Sample 1
98
76
0.775510
Sample 2
220
129
0.586364
Estimation for Difference
Difference
95% CI for Difference
0.189147
(0.083983, 0.294310)
CI based on normal approximation
Test
Null hypothesis
H₀: p₁ - p₂ = 0
Alternative hypothesis
H₁: p₁ - p₂ ≠ 0
Method
Z-Value
P-Value
Normal approximation
3.25
0.001
Fisher's exact
0.001
The test based on the normal approximation uses the pooled estimate of the proportion
(0.644654).
37. What is the Test Statistic? Z=3.25
38. What is the P-value? .001 39. What is your Conclusion of this analysis? Since the P-value is less than Alpha, we REJECT the null hypothesis and go in favor of the alternative hypothesis which states that there IS a difference between Democrats and Republicans who would vote for a 3
rd
party candidate in the population of ALL ETSU students. 40. Give a 95% confidence interval for the true difference in the proportion of Democrat students and the proportion of Republican students at ETSU who would consider voting for a third-party candidate. Insert Minitab evidence of the confidence interval here: Estimation for Difference
Difference
95% CI for Difference
0.189147
(0.083983, 0.294310)
CI based on normal approximation
41. Interpret your 95% confidence interval: We are 95% confident that the true difference in the population of Democrat and Republican students at ETSU who would consider voting for a 3
rd
party candidate is between 8.4% and 29.4%. In our sample of MATH-1530 students, there is a higher percentage of Democrats who say they would vote for a 3
rd
party candidate. Real Estate Sales
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The city tax assessor was interested in predicting residential home sales prices (Sales_Price) in a mid-western city as a function of finished square footage (Finished_Sq_Feet) of the home. Data on 522 home sales for the year 2002 were examined. X=Finished Square Feet Y=Sales-Price 42. Create an appropriate graph to display the relationship between Sales-Price and Finished-Sq-Feet. Insert the graph here: 43. Describe the association between these two variables: There is a positive and somewhat linear association between X and Y 44. Use Minitab to find the Correlation between these two variables: r =.819 Correlations
Sales_Price
Finished_Sq_Feet
0.819
45. Based on the graph and the correlation, how would you describe the Strength of this association? Moderately strong and linear 46. What is the least squares Regression Equation for predicting Sales-Price from Finished-Sq.-Feet? Show Minitab evidence here: FALL 2023 CAPSTONE DATA (3).MWX
Regression Analysis: Sales_Price versus Finished_Sq_Feet
The regression equation is
Sales_Price = - 81433 + 159.0 Finished_Sq_Feet
Model Summary
S
R-sq
R-sq(adj)
79122.9
67.15%
67.09%
Analysis of Variance
Source
DF
SS
MS
F
P
Regressio
n
1
6.65549E+1
2
6.65549E+1
2
1063.10
0.000
Error
520
3.25543E+1
2
6.26043E+0
9
Total
521
9.91091E+1
2
What is the Slope? +159 What is the y-intercept? -81,433 47. Interpret the Slope in relation to the variables: for every extra finished square foot in the house, the Sales Price increases by $159. 48. Use the regression equation to predict the Sales-Price of a home that has 2105 Finished-Sq.-Feet. Show your work: predicted Sales Price = -81433 + 159(2105)= 253,262 49. What percent of the variability in Sales-Price can be accounted for by the least squares linear regression on Finished-Sq.-Feet? (.819)(.819)=0.6708=67.08% which says that 67.8% of the variability in Sales Price can be explained by the square footage of the house.
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50. How well does the regression equation fit the data? The straight line is a good fit for this data, especially in the homes between 1000 and 3000 square feet BONUS +5 extra points: Other than a question that was asked on the Math 1530 Fall 2023 survey, can you come up with a question that you would find interesting to ask on a future survey?
I think a question that would be interesting would be “Are you taking college classes because you want this degree or are you taking college classes because your parents are making you”
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