ROBE Math 1530 - all sections Summer 2015 About the Summer 2015 Math 1530 Capstone project In the regular Fall and Spring semesters, the end-of-semester Math 1530 Capstone Project uses data collected from all Math 1530 students who responded to the survey in the given semester. This Summer 2015 Math 1530 Capstone project uses parts of the data from each of the two preceding semesters. The data is collected into a Minitab worksheet Summer 2015 1530 Capstone data.MTW 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 on d2l, under the Content tab. 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 to complete the work for your Summer 2015 1530 Capstone project, save it as a file titled Summer 2015 1530 Capstone Your Name and send in the document as an attachment to an email to Prof. Robe. It would be extraordinarily helpful if you highlighted or colored your answers. As always, the Math 1530 Capstone Project is worth 100 points, or 10%, of your overall Math 1530 grade. This assignment is due midnightish (end of the day) on Wednesday, 08JUL15. 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 on d2l - Prof Robe recommends you look at them for suggestions!!) with anyone, consult Minitab handouts, refer to our introduction-tocapstone 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. Graphs have titles. 'Histogram of C1' is not a title, and will cost you points. 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 semester. However, many problems are doable partway through the term. Don't leave the capstone until the last minute. Start working on it now. I can give helpful answers mid-term that I just won't have time for in the last week. Here are some of the questions that were asked on the surveys: Please note that the Summer data set includes parts of both the Fall 2014 and Spring 2015 survey data sets. In neither case did all of the survey data appear in a Capstone Project data file. This is just so you know where that data came from. From the Spring 2015 Math 1530 survey: GENDER_1: What is your gender? (Female, Male) AGE: What is your age (in years)? WEIGHT: What is your current weight (in pounds)? HEIGHT: What is your height in feet and inches? (These data have been changed to inches) NUCLEAR SAFETY: How safe would you feel if a nuclear energy plant were built near where you live? (Extremely safe, Very safe, Moderately safe, Slightly safe, Not at all safe) TALK POLITICS: How many days in a typical week do you talk about politics with family or friends? WASH HANDS: In a typical day, about how many times do you wash your hands? CLOTHING ARTICLES: How many articles of clothing are you wearing right now? CLOTHING PURCHASE: How much money did you spend on your last clothing purchase? (in US dollars) A total of 800 students responded to the MATH1530 class survey during the spring semester of 2015. From the Fall 2015 Math 1530 survey: GENDER: Are you male or female? (Male, Female) CHILDREN: What do you think is the ideal number of children for a family to have? MARRIED: What is your opinion about a married person having sexual relations with someone other than the marriage partner? (Always wrong, Almost always wrong, Wrong only sometimes, Not wrong at all) SEX: There's been a lot of discussion about the way morals and attitudes about sex are changing in this country. What is your opinion about two people having sexual relations before marriage? (Always wrong, Almost always wrong, Wrong only sometimes, Not wrong at all) PARTY: What political party do you identify with? (Democratic, Republican, Independent, Other) INCOME_TAX: Should Tennessee implement a state income tax? (Yes, No) DEATH_PENALTY: Do you favor or oppose the death penalty for persons convicted of murder? (Favor, Oppose) SLEEP: Usually, how many hours sleep do you get a night? A total of 1220 students responded to the MATH1530 class survey. The data for 1184 students were recorded for the survey data set. The Minitab worksheet Summer 2015 1530 Capstone data.MTW, C1: ID (an identification number given to each student in the data file) C2: GENDER_1 C3: AGE (yrs) C4: NUCLEAR SAFETY C5: TALK POLITICS C6: WASH HANDS C7: CLOTHING PURCHASE ($) C10: GENDER C11: MARRIED C12: PARTY C13: DEATH_PENALTY C14: SLEEP is set up as follows: Name: E number: Math 1530 section number MATH 1530 CAPSTONE TECHNOLOGY PROJECT SUMMER 2015 Problem 1: Identify Variable Type. One of these is a variable that is categorical and one is quantitative. Consider the different graphs that correspond to each variable type. Use Minitab to create two different graphs appropriate for each variable's type. EXTRA CREDIT if you can resize to fit all of the graphs on one page. NUCLEAR SAFETY TALK POLITICS Name: E number: Math 1530 section number Problem 2: Sampling. In the survey data, the variable \"AGE\" is the current age reported by each student. a. 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 (b). Then calculate the mean age of these first 10 observations and report the value below. N AGE (yrs) 1 2 3 4 b. The mean age of the first 10 students is 5 6 7 8 9 10 years. (Type the value into the space provided.) c. Identify the type of sampling method you have just used: d. Next, select a random sample of size n = 10 (Go to 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 C17-C18 into the \"Store samples in\" slot. Record the data for your sample in the table below. N ID AGE (yrs) 1 2 3 4 5 6 7 8 9 10 e. Calculate and report the mean age for your random sample of 10 students. The sample mean age is years. f. Identify the type of sampling method you have just used: g. REPEAT the random sample selection process three more times. Calculate and report the mean age for each random sample of 10 students. N ID AGE (yrs) 1 2 ii) The sample mean age is 3 4 years. 5 6 7 8 9 10 Name: E number: Math 1530 section number N ID AGE (yrs) 1 2 3 iii) The sample mean age is N ID AGE (yrs) 1 2 iv) The sample mean age is 4 5 6 7 8 9 10 5 6 7 8 9 10 years. 3 4 years. h. Suppose we think of all the students who responded to the survey as a population for the purposes of this problem. In that case, the population mean age is 21.293. Discuss (two or more complete sentences) the differences and similarities between 21.293 and the answers you got in (b), (e), and ii), iii), and iv). Name: E number: Math 1530 section number Problem 3(h): FLIP A COIN. Circle the outcome (Omit this page/problem if you got 'tails.') heads / tails. If you got 'heads,' then do this problem. Question 10 of the SPRING 2015 survey asked students, \"How much money did you spend on your last clothing purchase? (in US dollars)\" a. Create an appropriate graph to display the distribution of the variable called CLOTHING PURCASE and insert it here. b. Which of the following best describes the shape of the distribution? Underline your answer. Skewed left Symmetric Skewed right c. Using Minitab, calculate the basic statistics for the data collected on CLOTHING PURCASE. Copy and paste all of the Minitab output here. d. Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of CLOTHING PURCASE. Which statistic will you use to describe the center of the distribution? (Type name of the statistic here.) e. What is the value of that statistic? (Type value here.) f. Which statistic(s) will you use to describe the spread of the distribution? g. What is (are) the value(s) of that (those) statistic(s)? h. Look up the IQR rule on p. 50 in our textbook. Are there any outliers in this distribution? If so, what are their values? How many are there? Justify your answer. Name: E number: Math 1530 section number Problem 3(t): YOU JUST FLIPPED A COIN. If you got 'tails,' then do this problem. (Omit this page/problem if you got 'heads.') Question 12 of the FALL 2014 survey asked students, \"Usually, how many hours sleep do you get in a night?\" The data is in column 14 'SLEEP' of the data file. a. Create an appropriate graph to display the distribution of the variable called SLEEP and insert it here. b. Which of the following best describes the shape of the distribution? Underline your answer. Skewed left Symmetric Skewed right c. Using Minitab, calculate the basic statistics for the data collected on SLEEP and copy & paste the Minitab output here. d. Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of SLEEP. i) Which statistic will you use to describe the center of the distribution? (Type name of the statistic here.) ii) What is the value of that statistic? (Type value here.) iii) Which statistic(s) will you use to describe the spread of the distribution? iv) What is (are) the value(s) of that (those) statistic(s)? v) Look up the IQR rule on p. 50 in our textbook. Are there any outliers in this distribution? If so, what are their values? How many are there? Justify your answer. Name: E number: Math 1530 section number Problem 4: Age versus Handwashing. It is not surprising to see a fairly strong association between certain variables and age. On the SPRING 2015 Math 1530 survey, questions 3 and 7 asked students to give their age in years (AGE, yrs) and an estimate of how many times each day they wash their hands (WASH HANDS). We are specifically interested in seeing whether we can use a student's age to predict daily hand washes. a. Create an appropriate graph to display the relationship between AGE and WASH HANDS. 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 WASH HANDS. 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 WASH HANDS 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 daily hand washes for a student who is 20 years old. (Show your math.) Predicted hand washes = i. How well does the regression equation fit the data? Explain. Justify your answer with appropriate plot(s) and summary statistics. Name: E number: Math 1530 section number Problem 5 (both): FLIP A COIN TWICE. Circle the outcome of each toss: 1 heads/tails; 2 heads/tails. If you got heads both times or tails both times, then do this problem. (Omit this page/problem if you got one of each.) POLITICAL PARTY AND GENDER Question 5 from the FALL 2014 Math 1530 survey asked students \"What political party do you identify with?\" and Question 2 from that survey asked students \"What is your gender?\" The answers to these questions can be found in column 12 'PARTY' and column 10 'GENDER' in the Summer 2015 Capstone Data file. We want to check if there is a relationship between political party and gender among ETSU students. Assume the students who took the (Fall 2014 Math 1530) class survey are from an SRS of ETSU students. a. Create an appropriate graph to display the relationship between POLITICAL PARTY and GENDER. You don't want to display information for students that didn't answer both of these questions on the survey, so click on Data Options > Group Options and remove the checks in the boxes beside \"Include missing as a group\" and \"Include empty cells.\" Insert your graph here. b. Create an appropriate two-way table to summarize the data. Click on Options > Display missing values for... and put a dot in the circle beside \"No variables.\" Insert your table here. SUPPOSE WE SELECT ONE STUDENT AT RANDOM: (Calculate the following probabilities and show your work.) c. What is the probability that this student is both a male and Republican? P= d. What is the probability that this student is either a female or Independent? P= e. What is the probability that this student is a Democrat given that the student selected is a female? P= Name: E number: Math 1530 section number f. What is the probability that this student is a female given that the student is a Democrat? P= g. Do you think there may be an association between GENDER and POLITICAL PARTY? Why or why not? Explain your reasoning based on what you see in your graph. Name: E number: Math 1530 section number Problem 5 (mixed): YOU JUST FLIPPED A COIN TWICE. If you got one heads and one tails, then do this problem. (Omit this page/problem if you got two heads or two tails.) MARRIED AND DEATH_PENALTY Question 3 from the FALL 2014 Math 1530 survey asked students \"What is your opinion about a married person having sexual relations with someone other than the marriage partner?\" and Question 8 from the survey asked students \"Do you favor or oppose the death penalty for persons convicted of murder?\" The answers to these questions can be found in column 11 'MARRIED' and column 13 'DEATH_PENALTY' in the Summer 2015 Capstone Data file. We want to check if there is a relationship between MARRIED and DEATH_PENALTY among ETSU students. Assume the students who took the (Fall 2014 Math 1530) class survey are from an SRS of ETSU students. a. Create an appropriate graph to display the relationship between MARRIED and DEATH_PENALTY. You don't want to display information for students that didn't answer both of these questions on the survey, so click on Data Options > Group Options and remove the checks in the boxes beside \"Include missing as a group\" and \"Include empty cells.\" Insert your graph here. b. Create an appropriate two-way table to summarize the data. Click on Options > Display missing values for... and put a dot in the circle beside \"No variables.\" Insert your table here. SUPPOSE WE SELECT ONE STUDENT AT RANDOM: (Calculate the following probabilities and show your work.) c. What is the probability that this student is both opposed to the Death Penalty and says that sex with someone other than a marriage partner is 'not wrong at all'? P= d. What is the probability that this student favors the Death Penalty or says that sex with someone other than the marriage partner is 'always wrong'? P= e. What is the probability that this student is favors the death penalty given that the student says sex with someone other than the marriage partner is 'always wrong'? P= Name: E number: Math 1530 section number f. What is the probability that this student says that sex with someone other than the marriage partner is 'always wrong' given that the student favors the death penalty? P= g. Do you think there may be an association between DEATH PENALTY and MARRIED? Why or why not? Explain your reasoning based on what you see in your graph. Problem 6: The Statistic Brain Research Institute says that the average consumer spends about $59/month on women's clothes. http://www.statisticbrain.com/what-consumers-spend-each-month/ Do female ETSU students spend similar amounts on clothing? Name: E number: Math 1530 section number Spring 2015 Math 1530 survey question 10 asked \"How much money did you spend on your last clothing purchase? (in US dollars)\" We want data on just the female students. Minitab will separate the CLOTHING_PURCHASE data into two columns. Data > Unstack columns > Unstack the data in: CLOTHING PURCHASE, GENDER Using subscripts in: GENDER And you get a new worksheet, with the female clothing purchase data in its own column. a. Create a suitable graph to display the distribution of CLOTHING_PURCHASE reported by our sample of female college students and insert it here. Name: E number: Math 1530 section number b. Describe the distribution shown in your graph. c. Perform a test of significance to see if female college students have clothing spending habits similar to the average consumer. If this claim is true, then the average CLOTHING_PURCHASE reported by female students should be $59. For this test, the null hypothesis is that the average CLOTHING_PURCHASE reported by female students is what is reported for the average consumer. Thus, Ho: ?? = $59 per month Write the correct alternative hypothesis for the test. Ha: 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 hypothesis being tested. h. State your conclusion (words about females and clothing. USE COMPLETE SENTENCES. i. Is the P-value valid in this case? What assumptions are you making in order to carry out this test? Bonus Problem: Population males. According to the Census Bureau, http://quickfacts.census.gov/qfd/states/00000.html , in 2013, about 49.2.8% of the US population was male. Is the same true for the population of students at U.S. colleges and universities? On the Fall 2014 1530 Survey, question #1 asked our Math-1530 students \"What is your gender? (Female, Male)\" In the data worksheet, we call this variable GENDER the one in column 10. Name: E number: Math 1530 section number a. Create an appropriate graph to display the distribution of GENDER and insert it here. b. How many of the students surveyed said \"male?\" c. What proportion of our sample said \"male?\" d. Assume (for the purpose of this problem) that we may treat the Fall 2014 sample of Math-1530 students as a simple random sample drawn from the population of all U.S. college/university students. Use Minitab to calculate a 95% confidence interval for the proportion of students in the population who would say \"male\" to the survey question (based on our sample data). Copy and paste the Minitab output here. e. Interpret the confidence interval you reported in part (d). f. What do you think? Do our results contradict the claim made at the Census website or do they appear to agree with it? EXPLAIN