For this case study, we will use theTop_Colleges.xlsxfile, which consists of data from 95 top-ranked colleges.It includes variables regarding whether the college is public or private, the average annual out-of-state tuition and fees, and the average freshman SAT score (math + verbal only out of 1600).

Assigned Problem 1:For 2018, the average SAT score for incoming freshmen going to college in the United States was 1100.Perform a hypothesis test using a .05 significance level to test whether the top schools have an average SAT higher than the national average.State the conclusion in precise statistical language.

Assigned Problem 2:It is commonly believed that while public universities typically have tougher admission standards, private universities are often better academically.Perform a hypothesis test using a .05 significance level to determine whether fewer than 50% of the top-ranked universities are public.State the conclusion in precise statistical language.

Due at the end of Module 4

Course Learning Outcomes: 1, 2, 3 & 4

Top_Colleges.xlsx

Excel Instructions

Always start a hypothesis problem by stating the null and alternative hypothesis.We always assume the null is true, and the null always is stated mathematically with an equal sign.Add three rows to the top of the Excel spreadsheet so you may put your name and Module 4 at the top left corner.Starting on cell f4, write "Problem 1".On cell f5 and the following, state all the given information using the correct statistical symbol; i.e., = .05, so anyone seeing your solution can follow your logic.Solve these problems by finding the critical value (cv) and the standardized test statistic (STS) and/or calculating the p-value.Since this is a one-tail test, find the t-value for this right tailed test, which will be your cv.For the STS use the formula t = - ,s

a-bar is the sample mean, is the hypothesized mean; i.e., 1100, s is the sample standard deviation, and n is the sample size.You should calculate the p-value from the STS.Decide whether to reject for fail-to-reject the null.Now you are ready to state your conclusion.Remember, if you reject the null you start your conclusion by stating, "There is sufficient evidence to conclude . . ." , and if you fail-to-reject the null you start your conclusion by stating, "There is not sufficient evidence to conclude . . ."

Problem 2 uses categorical data therefore, we need to perform a hypothesis test for proportions.Again, always start by stating your null and alternative hypothesis.State the significance level as = .05.Find p-hat by using the "Sort & Filter" feature on Excel to sort the type of university; i.e., public or private, count the public ones and form your proportion of universities that are public.Since n*p > 5 and n*q > 5, we can use a normal distribution for our test.Find the cv.Find the STS with the formula

z = {(x) - p} / (pq) = (x - np) / (npq) =sample proportion - population proportion

[success failure / # in sample]

Since p and q are unknown, substitutingp and q is acceptable,p is the point estimate for p.

Using the same procedures as in Problem 1, state your conclusion.

9:58 1 5G AA A ythos.content.blackboardcdn.com C School Type Tuition Median SAT Princeton University Private 41820 1500 Harvard University Private 43938 1500 Yale University Private 45800 1500 Columbia University in the City of New York Private 51008 1480 Stanford University Private 45195 1475 University of Chicago Private 49380 1495 Massachusetts Institute of Technology Private 45016 1490 Duke University Private 47243 1455 University of Pennsylvania Private 47668 1445 California Institute of Technology Private 43362 1535 Dartmouth College Private 48108 1455 Johns Hopkins University Private 47060 1410 Northwestern University Private 47251 1460 Washington University in St Louis Private 6467 1050 Cornell University Private 47286 1415 Brown University Private 47434 1425 University of Notre Dame Private 46237 1430 Vanderbilt University Private 43838 1480 Rice University Private 10566 1445 University of California-Berkeley Public 35850 1375 Emory University Private 45008 1375 Georgetown University Private 674 405 University of California-Los Angeles Public 35583 1300 Carnegie Mellon University Private 49022 420 University of Southern California Private 48280 1375 Tufts University Private 48643 1445 Wake Forest University Private 46200 1330 University of Michigan-Ann Arbor Public 41906 1360 University of North Carolina at Chapel Hill Public 33418 1300 Boston College Private 47436 1355 New York University Private 46170 1350 College of William and Mary Public 39916 220 University of Rochester Private 46960 1350 Brandeis University Private 7558 1340 Georgia Institute of Technology-Main Campus Public 30698 1360 University of California-San Diego Public 36305 1220 Case Western Reserve University Private 4315 1360 University of California-Davis Public 36774 1210 Lehigh University Private 44890 1300 University of California-Santa Barbara Public 36743 1230 Boston University ivate $6664 1285 Northeastern University Private 1370 Rensselaer Polytechnic Institute Private 47908 1390 University of California-Irvine Public 36057 210 University of Illinois at Urbana-Champaign Public 29646 1350 University of Wisconsin-Madison Public 26660 1280 Pennsylvania State University-Main Campus Public 30452 195 University of Florida Public 28591 1265 Washington and Lee University Private 45617 1390 Yeshiva University Private 38730 1500 The University of Texas at Austin Public 34836 1255 George Washington University Private 48760 1150 Pepperdine University Private 46692 1225 Tulane University of Louisiana Private 48305 1320 Fordham University Private 45623 1255 Southern Methodist University Private 45940 1305 Syracuse University Private 41886 1155 University of Connecticut Public 32880 1230 Clemson University Public 31462 1245 Purdue University-Main Campus Public 28804 1150 University of Georgia Public 29046 1235 University of Maryland-College Park Public 29720 1300 University of Pittsburgh-Pittsburgh Campus Public 28168 1255 Texas A & M University-College Station Public 26583 1120 Worcester Polytechnic Institute Private 44222 1295 Rutgers University-New Brunswick Public 28591 1165 American University Private 41833 1260 Baylor University Private 38120 1225 University of Iowa Public 27409 170 University of Minnesota-Twin Cities Public 20810 1300 Virginia Polytechnic Institute and State University Public 28048 1295 Clark University Private 10730 1170 Indiana University-Bloomington Public 33241 980 Marquette University Private 35930 1175 Miami University-Oxford Public 30391 1185 Stevens Institute of Technology Private $536 1255 Texas Christian University Private 38600 1180 University of Delaware Public 30692 1205 University of Massachusetts Amherst Public 28998 190 Michigan State University Public 34965 1120 University of California-Santa Cruz Public 36275 1100 University of Vermont Public 37874 1185 Colorado School of Mines Public 33598 1295 Stony Brook University Public 21850 1255 The University of Alabama Public 24950 1130 University of Colorado Boulder Public 33151 1170 University of Denver Private 42090 1205 Drexel University Private 47051 1220 Florida State University Public 21673 1200 North Carolina State University at Raleigh Public 23551 1215 University of San Diego Private 42908 1215 Saint Louis University-Main Campus Private 37966 1200 University of Missouri-Columbia Public 24460 1165 University of Nebraska-Lincoln Public 22090 1170 University of New Hampshire-Main Campus Public 29532 1095 G