2.24 The National Survey of Student Engagement (NSSE) surveys freshmen and seniors about their level of engagement in campus and classroom activities that enhance learning. Hundreds of thousands of students from over 1,200 schools have completed surveys since 1999, the first year that the NSSE was administered. Among the many questions on the NSSE, students were asked how often they were assigned a paper of 20 pages or more during the academic year. For a sample of 19 institutions classified as national universities that made their data publicly available through the U.S. News & World ReportWeb site, here are the percentages of students who said they were assigned between 5 and 10 20-page papers: 0 5 3 3 1 10 2 2 3 1 2 4 2 1 1 1 4 3 5 a. Create a frequency table for these data. Include a third column for percentages. b. For what percentage of these schools did exactly 4% of their students report that they wrote between 2.26 Refer to the data in Exercise 2.24. a. Create a histogram of grouped data using 5 intervals. b. How many schools had 6% or more of their students reporting that they wrote between 5 and 10 20-page papers that year? c. How are the data distributed? 2.28 A university’s associate directors for whom a statistician was consulting were interested in alumni donations, as are many schools, not only because they want the money but also because it is one of the criteria by which U.S. News & World Report ranks U.S. institutions of higher learning. U.S. News includes this criterion because higher rates of alumni giving are seen as indicative of the satisfaction of former students. An increase in a school’s overall ranking by this magazine has been demonstrated to translate into an increase in applications— and all schools want that—even though there is controversy about the validity of these rankings. One set of rankings is for the best national universities: institutions that offer undergraduate, master’s, and doctoral degrees and have an emphasis on research. (Harvard tops the list that was published in 2005.) Here are the alumni giving rates that were reported in 2005; the rates are the percentages of alumni who donated to each of the top 70 national universities in the year prior to publication of these data. 48 61 45 39 46 37 38 34 33 47 29 38 38 34 29 29 36 48 27 25 15 25 14 26 33 16 33 32 25 34 26 32 11 15 25 9 25 40 12 20 32 10 24 9 16 21 12 14 18 20 18 25 18 20 23 9 16 17 19 15 14 18 16 17 20 24 25 11 16 13 a. How was the variable of alumni giving operationalized? What is another way that this variable could be operationalized? b. Create a grouped frequency table for these data. c. The data have quite a range, with the lowest scores belonging to Boston University, the University of California at Irvine, and the University of California at San Diego, and the highest belonging to Princeton University. What research hypotheses come to mind when you examine these data? State at least one research question that these data suggest to you. 2.30 Consider these three variables: finishing times in a marathon, number of university dining hall meals eaten in a semester on a three-meal-a-day plan, and scores on a scale of extroversion. a. Which of these variables is most likely to have a normal distribution? Explain your answer. b. Which of these variables is most likely to have a positively skewed distribution? Explain your answer, stating the possible contribution of a floor effect. c. Which of these variables is most likely to have a negatively skewed distribution? Explain your answer, stating the possible contribution of a ceiling effect. 2.32 The Centers for Disease Control and other organizations are interested in the health benefits of breastfeeding for infants. The National Immunization Survey includes questions about breast-feeding practices, including the question: “How long was [your child] breast- fed or fed breast milk?” The data for duration of breast-feeding in months for 20 hypothetical mothers are presented below. 0 7 0 12 9 3 2 0 6 10 3 0 2 1 3 0 3 1 1 4 a. Create a frequency table for these data. Include a third column for percentages. b. Create a grouped frequency table for these data with three groups (create groupings around the midpoints of 2.5 months, 7.5 months, and 12.5 months). 2.34 Refer to the data in Exercise 2.32. a. Create a frequency polygon of the original data. b. Create a frequency polygon of the grouped data. c. If you wanted the data to be normally distributed around 12 months, how would the data have to shift to fit that goal? How could you use knowledge about the current distribution to target certain women? 2.36 For each of the types of data described below, would you present individual data values or grouped data when creating a frequency distribution? Explain your answer clearly. a. Eye color observed for 87 people b. Minutes used on a cell phone by 240 teenagers c. Time to complete the Boston Marathon for the nearly 22,000 runners who participate d. Number of siblings for 64 college students d. Number of siblings for 64 college students 2.38 The director of career services at a large university is offering training on résumé construction. In an effort to present up-to-date information, using 23 résumés he just reviewed for a receptionist position in his office, he counts the total number of words used. Here are the data: 226 339 220 295 180 214 257 201 224 237 223 301 267 284 238 251 278 294 266 227 281 312 332 a. Create a grouped frequency table with 4 intervals. b. What does this information tell people who come to his training on résumé construction?