按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,*,案例分析,Harrigan大學學生背景之探討,指導教授：楊錦洲教授,學生：李佳璟,連豈浩,黃郁智,陳大翔,1,大綱,研究問題,研究背景,研究動機,案例敘述,題目探討,總結,2,研究問題,Harrigan大學對高中生來說是否比主要的競爭大學更具有選填志願的吸引力，並且能比主要的競爭大學更能吸引到名列前矛的學生。,3,研究背景,在這個年代大學林立，學生所能夠選擇的志願也相對的多，為了使學校能夠持續的發展，以及能夠吸收優良的學生使學校能夠保持競爭力。,4,研究動機,為了達到學校的持續發展和保持學校的競爭力這兩個主要的目的，所以對我們來說高中生是否對我們學校的興趣比我們的主要敵對大學還大。,5,案例敘述,6,案例敘述,Harrigan university is a liberal arts university in the Midwest that attempts to attract the highest quality students,especially from its region of the country.It has gathered data on 178 applicants who were accepted by Harrigan(a random sample from all acceptable applicants over the past several years).The data are in the file HARRIGAN.XLS.The variables are:,7,設定參數,Accepted:whether the applicant accepts Harrigans offer to enroll,MainRival:whether the applicant enrolls at Harrigans main rival university,HSClubs:number of high school clubs applicant served as an officer,HSSports:number of varsity letters applicant earned,HSGPA:applicants high school GPA,HSSize:number of students in applicants graduating class,SAT:applicants combined SAT score,CombinedScore:a combined score for the applicant used by Harrigan to rank applicant,8,案例敘述,The derivation of the combined score is a closely kept secret by Harrigan,but it is basically a weighted average of the various components of high school performance and SAT.Harrigan is concerned that it is not getting enough of the best students,and worse yet,it is concerned that many of these best students are going to Harrigans main rival.Solve the following problems and then,based on your analysis,comment on whether Harrigan appears to have a legitimate concern.,9,題目探討,10,第一題,Find a 95%confidence interval for the proportion of all acceptable applicants who accept Harrigans invitation to enroll.Do the same for all acceptable applicants with a combined score less than 330;with a combined score greater than 375.(Note that 330 and 375 are approximately the first and third quartiles of the Score variable.),11,求出交集,N Mean StDev SE Mean,103 345.72 30.02 2.96,95%CI,(339.92,351.52),330以下和95%信賴區間的交集為0。,375以上和95%信賴區間的交集為0。,12,第一題結論,第一小題，主要是要讓我們了解到，錄取生的成績分佈，我們看這個圖可以看到落在四分位差和信賴區間中間的人數分布。此外我們再補充個圓餅圖，來更了解到整體的分佈,13,第二題,Find 95%confidence intervals for the mean combined score,the mean high school GPA,and the mean SAT score of all acceptable students who accept Harrigans invitation to enroll.Do the same for all acceptable students who choose to enroll elsewhere.Then find 95%confidence intervals for the differences between these means,where each difference is a mean for students enrolling at Harrigan minus the similar mean for students enrolling elsewhere.,14,1.CombinedScore比較,Two-sample T for C12 vs C13,N Mean StDev SE Mean,C12 104 346.4 30.7 3.0,C13 28 376.1 24.6 4.6,Difference=mu(C12)-mu(C13),Estimate for difference:-29.71,95%CI for difference:,(-40.82,-18.60),T-Test of difference=0(vs not=):T-Value=-5.37 P-Value=0.000 DF=52,15,2.SAT比較,Two-sample T for C15 vs C16,N Mean StDev SE Mean,C15 103 1180 135 13,C16 28 1189 130 24,Difference=mu(C15)-mu(C16),Estimate for difference:-9.0,95%CI for difference:,(-65.2,47.1),T-Test of difference=0(vs not=):T-Value=-0.32 P-Value=0.748 DF=44,16,3.GPA比較,Two-sample T for C18 vs C19,N Mean StDev SE Mean,C18 103 84.60 7.34 0.72,C19 28 87.37 5.92 1.1,Difference=mu(C18)-mu(C19),Estimate for difference:-2.76,95%CI for difference:,(-5.44,-0.09),T-Test of difference=0(vs not=):T-Value=-2.07 P-Value=0.043 DF=51,17,第二題結論,一開始我們先以總和分數來做分析，很明顯的發現，,Harrigan,的總和分數輸對方一節，因此我們再把它拆開成學測分數和平時分數來看，學測分數的表現上，,Harrigan,和競爭大學幾乎相差無幾，可是在平時成績上就輸了不少，所以想要在招收更優秀的學生的話，在平時成績上的入學要求，要在更加的提高。,18,第三題,Harrigan is interested(as are most schools)in getting students who are involved in extracurricular activities(clubs and sports).Does it appear to be doing so?Find a 95%confidence interval for the proportion of all students who decide to enroll at Harrigan who have been officers of at least two clubs.Find a similar confidence interval for those who have earned at least four varsity letters in sports.,19,體保生分數的信賴區間,The assumed standard deviation=24.84,N Mean StDev SEMean,60 358.85 24.84 3.21,95%CI,(352.56,365.14),20,體保生和全部學生的分數比較圖,N Mean StDev Mean,SPORT 60 1173 140 18,SAT 103 1180 135 13,Difference=mu(SPORTSAT)-mu(SAT),Estimate for difference:-7.5,95%CI for difference:,(-52.0,36.9),T-Test of difference=0(vs not=):T-Value=-0.34 P-Value=0.738 DF=119,21,第三題結論,這題我們求出了，體育優良的學生綜合分數的信賴區間。此外我們還另外把體育優良的學生的學測成績，和所有學生的學測成績做比較，發現在學測成績上，學生們的成績幾乎相差無幾。也就是說，目前Harrigan大學，對於招收體育較為優良學生的方案可以說是非常的成功。,22,第四題,The combined score Harrigan calculates for each student gives some advantage to students who tank highly in a small high school.Therefore,Harrigan wonders whether it is relatively more successful in attracting students from large high school.Develop one or more confidence intervals for relevant parameters shed some light on this issue.,23,區分大小學校,Variable N N*Mean SE Mean,C12 103 0 266.1 10.9,StDev Minimum Q1 Median Q3,110.7 45.0 193.0 271.0 346.0,以平均數266做區分出大小學校,24,1.大小學校的GP