Your name: Your Summer 2017 Math 1530 Section number: Your E number: MATH 1530 CAPSTONE TECHNOLOGY PROJECT SUMMER 2017 Problem 1: Identify Variable Type. Which of these questions from the class survey produced variables that are categorical and which are quantitative? Use your word processor to color, underline, or highlight the best option. a. ANTHEM Categorical Quantitative State an appropriate plot for this variable: b. CLASS Categorical Neither . Quantitative Neither State an appropriate plot for this variable: c. STATES Categorical . Quantitative State an appropriate plot for this variable: Neither . Your Summer 2017 Math 1530 Section number: Your name: Your E number: Problem 2: Sampling. In the survey data, the variable \"AGE\" is the current age reported by each student. a. Pretend for a minute that the students who responded to the survey are a complete population in and of themselves. {This is not really true, but for the sake of argument, pretend.} In that case, Stat > Basic Statistics > Display Descriptive Statistics > Variables: AGE will generate population parameters for 'AGE.' Copy and display all of the Minitab output here. b. The population mean for the AGE data is . c. Type the first 10 observations from the column representing the variable AGE into the table below, and use this as your sample data for part (d). Then calculate the mean age of these first 10 observations and report the value below. N 1 2 3 4 5 6 7 8 9 10 AGE (yrs) d. The sample mean age of the first 10 students is value into the space provided.) years. (Type the e. Identify the type of sampling method you have just used: ______________________ f. Next, select a random sample of size n = 10 Calc > Random Data > Sample from Columns. Type the number 10 in the \"Number of rows to Sample\" slot. Enter the variable \"ID\" and \"AGE\" into the \"From columns\" slot. Enter C20-C21 into the \"Store samples in\" slot. Record the data for your sample in the table below. Your Summer 2017 Math 1530 Section number: Your name: N 1 2 3 4 5 6 Your E number: 7 8 9 10 ID AGE (yrs) g. Calculate and report the mean age for your random sample of 10 students. The sample mean age is years. h. Identify the type of sampling method you have just used: _________________________ i. Discuss (two or more complete sentences) the differences and similarities between the population mean and the sample mean answers you got in (b), (d) and (g). Your Summer 2017 Math 1530 Section number: Your name: Your E number: Problem 3(e): If your E number ends in an even number (0, 2, 4, 6, or 8) then do this question. (Omit this page/problem if your E# ends with an odd number.) A question on the SPRING 2017 survey asked students, \"Approximately, how many miles do you live from campus? (Enter 0 if you live on campus.) \" a. Create an appropriate graph to display the distribution of the variable called MILES and insert it here. b. Which of the following best describes the shape of the distribution? Underline (or highlight) your answer. Skewed left Symmetric Uniform Skewed right Bimodal c. Using Minitab, calculate the basic statistics for the data collected on MILES. Copy and paste all of the Minitab output here. Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of MILES. d. Which statistic will you use to describe the center of the distribution? __________. e. In one or two sentences, describe why this statistic was chosen. f. What is the value of that statistic? . Your name: Your Summer 2017 Math 1530 Section number: Your E number: g. Which statistic(s) will you use to describe the spread of the distribution? _______________ h. What is (are) the value(s) of that (those) statistic(s)? _________ i. Are there any outliers in this distribution? Justify your answer using the IQR rule or an appropriate plot. Problem 3(o): If your E number ends in an odd number (1, 3, 5, 7, or 9) then do this question. (Omit this page/problem if your E# ends with an even number.) A question on the SPRING 2017 survey asked students, \"Approximately, how much do you spend on gas (in U.S. dollars) a week?\" a. Create an appropriate graph to display the distribution of the variable called GAS and insert it here. b. Which of the following best describes the shape of the distribution? Underline (or highlight) your answer. Skewed left Symmetric Uniform Skewed right Bimodal c. Using Minitab, calculate the basic statistics for the data collected on GAS. Copy and paste all of the Minitab output here. Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of GAS. d. Which statistic will you use to describe the center of the distribution? . Your name: Your Summer 2017 Math 1530 Section number: Your E number: e. In one or two sentences, describe why this statistic was chosen. f. What is the value of that statistic? . g. Which statistic(s) will you use to describe the spread of the distribution? . h. What is (are) the value(s) of that (those) statistic(s)? . i. Are there any outliers in this distribution? Justify your answer using the IQR rule or an appropriate plot. Problem 4: RELIGION versus FAV NUMBER. One survey question asked students, \"What is your favorite whole number between 0 and 50? \" Another question asked students, \"What is your religious identification? (Protestant/Other Christian, Catholic, Mormon, Jewish, Muslim, Other Non-Christian religion, None/Atheist/Agnostic) \" a. Create a suitable graph to display the distribution of RELIGION and insert it here. b. What is the mode of this distribution? (Please underline one option.) Protestant/Other Christian Muslim Catholic Other Non-Christian religion Mormon Jewish None/Atheist/Agnostic c. Create a side-by-side boxplot to display the FAV_NUMBER of students for the different levels of RELIGION. (Go to Graph > Boxplot > One Y with Groups > OK. Select FAV_NUMBER for the \"Graph variables\" slot and RELIGION for the \"Categorical variables for grouping\" slot.) Insert your graph here. Your name: Your Summer 2017 Math 1530 Section number: Your E number: Use the side-by-side boxplot found in part (c) to answer the following questions. d. Which religious affiliation has the student with the highest favorite number? . e. Which religious affiliation has the student with the lowest favorite number? . f. Which religious affiliation has the largest IQR? . Your name: Your Summer 2017 Math 1530 Section number: Your E number: Problem 5: AGE vs. FAV_NUMBER. On the SPRING 2017 Math 1530 survey, one question asked students \"What is your age (in years)?\" Another question asked \"What is your favorite whole number between 0 and 50? \" We are interested in seeing whether we can use AGE to predict (favorite) FAV_NUMBER. a. Create an appropriate graph to display the relationship between AGE and FAV_NUMBER. Insert it here. b. Does the plot show a positive association, a negative association, or no association between these two variables? EXPLAIN what this means with respect to the variables being studied. c. Describe the form of the relationship between AGE and FAV_NUMBER. d. Report the value of the correlation between this pair of variables? r = . e. Based on the information displayed in the graph and the correlation you just reported, how would you describe the strength of the association? f. Using Minitab, obtain the equation for the least squares regression of FAV_NUMBER on AGE. Copy & paste the output here. g. Interpret the value of the slope in the least squares regression equation you found in part (f). h. Use the regression equation in part (f) to predict the favorite number for a 20 year old student. (Show your math.) Predicted number = i. How well does the regression equation fit the data? Explain. Justify your answer with appropriate plot(s) and summary statistics. Your name: Your Summer 2017 Math 1530 Section number: Your E number: Problem 6: GENDER and FACULTY_WEAPONS A question from the FALL 2016 Math 1530 survey asked students \"What gender do you identify with? (Female, Male, Other) \" and another question asked students, \"Do you agree with ETSU faculty and staff being able to carry concealed weapons on campus? (Agree, Disagree)\" We want to check if there is a relationship between GENDER and FACULTY_WEAPON among ETSU students. Assume the students who took the (Fall 2016 Math 1530) class survey are from an SRS of ETSU students. a. Create an appropriate graph to display the relationship between GENDER and FACULTY_WEAPON. Insert your graph here. b. Create an appropriate two-way table to summarize the data. Insert your table here. (IN MINITAB: STAT TABLES CROSS TABULATION AND CHI-SQUARE. Make sure to select \"Options\" and click \"No variables\" under the Display missing values for\"). SUPPOSE WE SELECT ONE STUDENT AT RANDOM: (Calculate the following probabilities and show your work.) c. What is the probability that this student identifies as female and agrees with faculty being allowed to carry weapons on campus? P = d. What is the probability that this student identifies as female or agrees with faculty being allowed to carry weapons on campus? P = e. What is the probability that this student does not identify as female given that the student does not agree with faculty being allowed to carry weapons on campus? P = f. What is the probability that this student does not agree with faculty being allowed to carry weapons on campus given that the student does not identify as female? Your name: P = Your Summer 2017 Math 1530 Section number: Your E number: Your name: Your Summer 2017 Math 1530 Section number: Your E number: Problem 7: MARIJUANA In Tennessee, the fine for first-time offense possession of less than oz of marijuana is a mandatory $250 (http://norml.org/laws/item/tennessee-penalties-2). A question on the Fall 2016 Math 1530 survey asked students \"If a student is caught on campus with marijuana, how much should that student be fined? (in US dollars) \" How well do students' ideas about marijuana fines line up with the mandatory penalty? a. Create a suitable graph to display the distribution of MARIJUANA reported by our sample of college students and insert it here. b. Perform a test of significance to see if ETSU college student's marijuana fine is, on average, the same amount as the mandatory penalty. If this is true, then the average MARIJUANA suggested by ETSU students should be $250. Thus, Ho: = 250 dollars Write the correct alternative hypothesis for the test: . d. Use Minitab to perform the appropriate test. Copy and paste the output for the test here. e. What is the name of your test statistic and what is its value? f. What is the P-value for the test? P = . g. State your decision regarding the hypotheses being tested. h. State your conclusion. USE COMPLETE SENTENCES. i. Is the P-value valid in this case? What assumptions are you making in order to carry out this test? . ROBE Math 1530 - 901 09JUN17 About the Summer 2017 Math 1530 Capstone project The Summer Math 1530 Capstone Project uses data collected from Math 1530 students who responded to surveys in the Fall 2016 and Spring 2017 semesters. The data is collected into a Minitab worksheet, accessible as a separate Minitab file. Both the actual assignment and the Minitab data file i) will be sent to each student as an email attachment, ii) have been attached to a d2l News item, and iii) have been posted under the Content tab on d2l. You WILL NEED TO USE MINITAB to answer most of the questions. You WILL NEED TO OPEN THE MINITAB WORKSHEET FILE USING MINITAB. There is a whole module of Minitab handouts on the d2l site for your Robe's Math 1530 class, under the Content tab. There are also copies of several previous capstones, AND THEIR SOLUTIONS through a link under the Content tab on D2L. SHOW YOUR WORK and DO YOUR OWN WORK where appropriate, but you should use a word processor to write up your results. The Capstone document has a header on each page. Double click the header (the grey print at the top of the page: Name, E-number, etc). Enter your name and the information listed. Then click \"Close header and footer\" in the menu list. This will put your name, etc, at the top of each page of the Capstone project. LEAN ON Minitab for as much of the work as possible. Word process your answers, and copy-and-paste Minitab's output (where necessary) into the Capstone Project document. A numbered list of answers (separate from the questions) is not acceptable. Handwritten copy of Minitab output is not acceptable. You are free to send in the document electronically or to print it out and hand it in to Prof. Robe's office. It would be extraordinarily helpful if you highlighted or colored or changed the font of your answers. The easier your work is to grade (because it follows my formatting instructions), the better off your grade will be!! The Math 1530 Capstone Project is worth 100 points, or 10%, of your overall Math 1530 grade. Per Dept of Mathematics and Statistics policy, this assignment is due at 5 pm on Wednesday, 05JUL17. These deadlines are firm, as we are all busy during the week of Final Exams. A late Capstone project will lose 5 points per hour (or part of an hour) that it is late. This specifically includes lateness due to weather and technology failure outside of your control. Each student should do their own work. If two people get the same question wrong the same way, neither of them will get credit for the question and we will consider together the joys of Academic Misconduct paperwork on file with the Dean of Arts and Sciences! On the other hand, you are absolutely free to discuss any old capstone and its solution (several are posted through a link on d2l - Prof Robe recommends you look at them for suggestions!!) with anyone, consult Minitab handouts, refer to our introduction-to-capstone assignments, ask Prof. Robe, etc. When you submit the Capstone assignment, start each question on a new page( this is part of the credit!!). Where graphs are required, insert the graph into the problem it goes with, NOT at the end of the page or the end of the document. I will not go looking among loose pages a, b, and c for the graph that belongs on page d. Where other information from Minitab is required, submit only the information needed in the problem. Do not submit everything Minitab spits out, hoping the right answer is there somewhere. If you haven't seen-that-graph in class - DON'T USE IT on the Capstone. If I have to spend time searching for your answer, it cuts down on the time I have to thoughtfully consider partial credit, so you will get less of it. Please note that the capstone uses virtually all of our Math 1530 chapters. Some of the problems will not be doable until nearly the end of the term. However, many problems are doable right now. Don't leave the capstone until the end. Start working on it now. I can give helpful answers now that I just won't have time for in early July. Here are the questions that were asked on the surveys: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. AGE: What is your age (in years)? CLASS: What is your classification in college? (Freshman/first-year, Sophomore, Junior, Senior) CHILDREN: What is your ideal number of children? CALLS: Approximately, how many phone calls do you make per day? TEXTS: Approximately, how many text messages, including Group Me messages, do you send per day? MILES: Approximately, how many miles do you live from campus? (Enter 0 if you live on campus.) GAS: Approximately, how much do you spend on gas (in U.S. dollars) a week? NUMBER: What is your favorite whole number between 0 and 50? LGBT: In the U.S., more Americans are identifying as LGBT. Do you, personally, identify as lesbian, gay, bisexual, or transgender? (Yes, No) GUNS: Are you satisfied with America's law or policies on guns? (Yes, No) TERROISM: Are you satisfied with America's security with terrorism? (Yes, No) RELATIONS: Are you satisfied with America's state of race relations? (Yes, No) RELIGION: What is your religious identification? (Protestant/Other Christian, Catholic, Mormon, Jewish, Muslim, Other Non-Christian religion, None/Atheist/Agnostic) The combined responses to the Fall 2016 and Spring 2017 Math 1530 class surveys included close to 1500 students. A usable subset of that data for use in this project is included in the data file Summer 2017 Capstone Data.MTW. The Minitab worksheet, Summer 2017 Capstone Data.MTW , is set up as follows: C1: ID (an identification number given to each student in the data file) C2: ANTHEM C3: STATES C4: AGE C5: CLASS C6: MILES C7: GAS C8: PHONE_CALLS C9: RELIGION C10: FAV_NUMBER C11: GENDER C12: FACULTY_WEAPONS C13: MARIJUANA