Math 181 Statistics TR Take Home Exam 4 Helgeson (Spring 2016) Name________________________________ You may not receive help on this Take Home Exam from the Math Resource Center Tutors. 1. Label each of the scatterplots below with one of the following statements: (a) Strong, positive linear correlation (b) Strong, negative linear correlation (c) Moderate, positive linear correlation (d) Moderate, negative linear correlation (e) No linear correlation (i) (ii) (iv) (iii) (v) You may not receive help on this Take Home Exam from the Math Resource Center Tutors. Take Home Exam 4 2. One of your instructor's classes took their Final Exam on the Monday of Final Exam week during the Fall 2015 semester. Many JCCC students work part-time and full-time jobs while attending school. Your instructor is interested in seeing if there is a linear relationship between the number of hours a student works during the weekend prior to a Monday Final Exam and the score the student earns on his/her Final Exam. The data is included in the table below: Hours Final Exam worked Score 0 96 4 87 12 75 5.25 80 0 88 25 67 (a) Make a scatterplot for this data and determine if there is a linear relationship between the variables. Is there a linear relationship between the variables? Yes or No (b) Which variable should be your predictor variable? 13 86 3.5 81 18 79 6 82 9.5 83 11.25 70 16 74 20 68 22.5 70 (c) Which variable should be your response variable? 2 Take Home Exam 4 You may not receive help on this Take Home Exam from the Math Resource Center Tutors. 2. (Continued) (d) If there is a linear relationship, find the linear correlation coefficient and interpret this value. (e) If there is a linear relationship, calculate the regression line. Write the equation using words in place of x and y . Round your equation values to two decimal places. (f) If you calculated a regression line, interpret the slope in the context of this problem. (g) If there is a linear relationship, find the coefficient of determination and interpret this value. 3 This page was intentionally left blank. 4 Take Home Exam 4 2. You may not receive help on this Take Home Exam from the Math Resource Center Tutors. (Continued) (h) If this data has a linear relationship, then number of hours worked on the weekend before a Monday final can be used to predict the score on the final exam. If you calculated a regression line in part (e), use it to predict the final exam score for a student who worked 10 hours the weekend before his/her Monday exam. Round your answer to the nearest whole number. If you calculated a regression line in part (e), use it to predict the final exam score for a student who worked 17 hours the weekend before his/her Monday exam. Round your answer to the nearest whole number. 5 Take Home Exam 4 You may not receive help on this Take Home Exam from the Math Resource Center Tutors. 3. Mars, Inc. manufactures M&M's, one of the most popular candy treats in the world. The milk chocolate candies come in a variety of colors including blue, brown, green, orange, red, and yellow. According to the M&M website, the overall percentages for each of the colors is shown in the table on the left below. A random sample of multiple bags of M&M milk chocolates were opened and the color counts from the bags are shown in the table on the right below. Color Percentage Blue 24% Brown 13% Green 20% Orange 16% Red 13% Yellow 14% 100% Color Frequency Blue 105 Brown 72 Green 89 Orange 84 Red 70 Yellow 80 500 Does the sample provide sufficient evidence at a 5% significance level to conclude that the distribution in the proportions of M&M colors is different from the overall percentages reported on the M&M website? Be sure to state your hypotheses, check that any Central Limit Theorem criteria are met, give the test statistic and P-value, and then state your decision in context. If you need more space, use the next page 6 Take Home Exam 4 You may not receive help on this Take Home Exam from the Math Resource Center Tutors. 4. Using data collected from the FBI and the Bureau of Alcohol, Tobacco, and Firearms, measures of statistics showed that for the different states, there is a positive, linear correlation between the number of registered automatic weapons and the murder rate. Can we conclude that an increase in the number of registered automatic weapons will cause an increase in the murder rate? Explain why or why not. 7 Take Home Exam 4 You may not receive help on this Take Home Exam from the Math Resource Center Tutors. 5. The following table gives the distribution of grades for three professors at JCCC who have taught the Math 205 course over multiple semesters. Students wonder if any of these professors has a tendency to give higher grades in general than the other two professors. Grade Professor Gilson McElroy Townsend Total A 18 28 35 81 B 25 56 40 121 C 85 70 73 228 D and F 17 18 15 50 Total 145 172 163 480 Using a 5% significance level to test and see if there is an association between professor and the grade that students receive. Be sure to state your hypotheses, check that any Central Limit Theorem criteria are met, give the test statistic and P-value, and then state your decision in context. If you need more space, use the next page 8 Take Home Exam 4 You may not receive help on this Take Home Exam from the Math Resource Center Tutors. 6. In our Group in StatCrunch is the data from when we collected the Body Parts data in class. The data set is titled \"Body Parts (Spring 2016)\". Recall that on the day we collected data, all students measured their height, head circumference, and forearm length in centimeters (cm). The data set in StatCrunch is for all three of Helgeson's Statistics classes this semester. (a) Make a scatterplot comparing Head Circumference and Height and determine if there is a linear relationship between the two variables. Is there a linear relationship between these two variables? Yes or No (b) Make a scatterplot comparing Forearm Length and Height and determine if there is a linear relationship between the two variables. Is there a linear relationship between these two variables? Yes or No 9 Take Home Exam 4 You may not receive help on this Take Home Exam from the Math Resource Center Tutors. 6. (Continued) (c) If there is a linear relationship between Head Circumference and Height , find the linear correlation coefficient and interpret this value. (d) If there is a linear relationship between Head Circumference and Height, calculate the regression line using Head Circumference as the predictor variable for Height. Write the equation using words in place of x and y . Round your equation values to three decimal places. (e) If there is a linear relationship between Forearm Lenght and Height , find the linear correlation coefficient and interpret this value. (f) If there is a linear relationship between Forearm Length and Height, calculate the regression line using Forearm Length as the predictor variable for Height. Write the equation using words in place of x and y . Round your equation values to three decimal places. (g) Determine which variable (Head Circumference or Forearm Length) is the better predictor of Height. Explain how you made this determination. 10 Take Home Exam 4 You may not receive help on this Take Home Exam from the Math Resource Center Tutors. 6. (Continued) (h) Interpret the slope of the regression line for the variable pairing that is the better predictor. Be sure your interpretation includes the context of this problem. (i) Find the coefficient of determination for the variable pairing that is the better predictor. Interpret this value in the context of the problem. 11