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 22 3 1 2 4 2 11 1 4 3 5a. Create a frequency table for these data. Include athird column for percentages.b. For what percentage of these schools did exactly4% of their students report that they wrote between2.26 Refer to the data in Exercise 2.24.a. Create a histogram of grouped data using 5intervals.b. How many schools had 6% or more of their studentsreporting that they wrote between 5 and 1020-page papers that year?c. How are the data distributed?2.28 A universitys associate directors for whom a statisticianwas consulting were interested in alumni donations,as are many schools, not only because they wantthe money but also because it is one of the criteria bywhich U.S. News & World Report ranks U.S. institutionsof higher learning. U.S. News includes this criterion becausehigher rates of alumni giving are seen as indicativeof the satisfaction of former students. An increasein a schools overall ranking by this magazine has beendemonstrated to translate into an increase in applicationsand all schools want thateven though there iscontroversy about the validity of these rankings. Oneset of rankings is for the best national universities: institutionsthat offer undergraduate, masters, and doctoraldegrees and have an emphasis on research.(Harvard tops the list that was published in 2005.) Hereare the alumni giving rates that were reported in 2005;the rates are the percentages of alumni who donated toeach of the top 70 national universities in the year priorto publication of these data.48 61 45 39 46 37 38 34 33 4729 38 38 34 29 29 36 48 27 2515 25 14 26 33 16 33 32 25 3426 32 11 15 25 9 25 40 12 2032 10 24 9 16 21 12 14 18 2018 25 18 20 23 9 16 17 19 1514 18 16 17 20 24 25 11 16 13a. How was the variable of alumni giving operationalized?What is another way that this variable couldbe operationalized?b. Create a grouped frequency table for these data.c. The data have quite a range, with the lowest scoresbelonging to Boston University, the University ofCalifornia at Irvine, and the University of Californiaat San Diego, and the highest belonging toPrinceton University. What research hypothesescome to mind when you examine these data? Stateat least one research question that these data suggestto you.2.30 Consider these three variables: finishing times in amarathon, number of university dining hall meals eatenin a semester on a three-meal-a-day plan, and scoreson a scale of extroversion.a. Which of these variables is most likely to have anormal distribution? Explain your answer.b. Which of these variables is most likely to have apositively skewed distribution? Explain your answer,stating the possible contribution of a floor effect.c. Which of these variables is most likely to have anegatively skewed distribution? Explain your answer,stating the possible contribution of a ceilingeffect.2.32 The Centers for Disease Control and other organizationsare interested in the health benefits of breastfeedingfor infants. The National Immunization Surveyincludes questions about breast-feeding practices, includingthe question: How long was [your child]breast- fed or fed breast milk? The data for duration ofbreast-feeding in months for 20 hypothetical mothersare presented below.0 7 0 12 9 3 2 0 6 103 0 2 1 3 0 3 1 1 4a. Create a frequency table for these data. Include athird column for percentages.b. Create a grouped frequency table for these datawith three groups (create groupings around themidpoints of 2.5 months, 7.5 months, and 12.5months).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 distributedaround 12 months, how would the data have to shiftto fit that goal? How could you use knowledgeabout the current distribution to target certainwomen?2.36 For each of the types of data described below, wouldyou present individual data values or grouped data whencreating a frequency distribution? Explain your answerclearly.a. Eye color observed for 87 peopleb. Minutes used on a cell phone by 240 teenagersc. Time to complete the Boston Marathon for thenearly 22,000 runners who participated. Number of siblings for 64 college studentsd. Number of siblings for 64 college students2.38 The director of career services at a large university isoffering training on r?sum? construction. In an effortto present up-to-date information, using 23 r?sum?s hejust reviewed for a receptionist position in his office,he counts the total number of words used. Here are thedata:226 339 220 295 180 214 257 201224 237 223 301 267 284 238 251278 294 266 227 281 312 332a. Create a grouped frequency table with 4 intervals.b. What does this information tell people who come to his training on r?sum? construction?