In R Studio:

a$.$ Which statistical test is most appropriate for comparing debt at graduation incurred by students at private universities and public colleges?

b$.$ At the a$=0\mathrm{.}05$ level and assuming that the population is normally distributed, is there significant evidence that the two types of universities result in different debt levels?

Option Average.Debt.At$.$Graduation

$1$ Private $8577$

$2$ Private $19104$

$3$ Private $16723$

$4$ Private $21506$

$5$ Private $15521$

$6$ Private $25528$

$7$ Private $20677$

$8$ Private $21238$

$9$ Private $22197$

$10$ Private $23485$

$11$ Private $19135$

$12$ Private $25167$

$13$ Private $26983$

$14$ Private $24394$

$15$ Private $27237$

$16$ Private $26157$

$17$ Private $23067$

$18$ Private $21291$

$19$ Private $24702$

$20$ Private $20849$

$21$ Private $24243$

$22$ Private $23051$

$23$ Private $26185$

$24$ Private $15720$

$25$ Private $36546$

$26$ Private $36626$

$27$ Private $34940$

$28$ Private $27925$

$29$ Private $28048$

$30$ Private $30873$

$31$ Private $29547$

$32$ Private $33588$

$33$ Private $27407$

$34$ Private $33792$

$35$ Private $30850$

$36$ Private $19000$

$37$ Private $22364$

$38$ Private $29459$

$39$ Private $30742$

$40$ Private $23772$

$41$ Private $33081$

$42$ Private $30480$

$43$ Private $32040$

$44$ Private $31622$

$45$ Private $30879$

$46$ Private $31444$

$47$ Private $28562$

$48$ Private $32077$

$49$ Private $26451$

$50$ Private $40365$

$51$ Private $26321$

$52$ Private $21067$

$53$ Private $34820$

$54$ Private $30569$

$55$ Private $32394$

$56$ Private $33487$

$57$ Private $25621$

$58$ Private $28953$

$59$ Private $35740$

$60$ Private $26722$

$61$ Private $25069$

$62$ Private $22543$

$63$ Private $29947$

$64$ Private $40721$

$65$ Private $28464$

$66$ Private $31000$

$67$ Private $35520$

$68$ Private $40403$

$69$ Private $31013$

$70$ Private $32943$

$71$ Private $30487$

$72$ Private $37048$

$73$ Private $34865$

$74$ Private $37008$

$75$ Private $29297$

$76$ Private $32071$

$77$ Private $31784$

$78$ Private $39167$

$79$ Private $30826$

$80$ Private $29455$

$81$ Private $28093$

$82$ Private $30830$

$83$ Private $36500$

$84$ Private $27857$

$85$ Private $38198$

$86$ Private $28477$

$87$ Private $34375$

$88$ Private $34803$

$89$ Private $28598$

$90$ Private $35627$

$91$ Private $28149$

$92$ Private $30658$

$93$ Private $37740$

$94$ Private $38780$

$95$ Private $36625$

$96$ Private $32131$

$97$ Private $25770$

$98$ Private $29000$

$99$ Private $33870$

$100$ Private $39771$

$101$ Public $20127$

$102$ Public $24905$

$103$ Public $17869$

$104$ Public $26017$

$105$ Public $26034$

$106$ Public $21596$

$107$ Public $21028$

$108$ Public $26818$

$109$ Public $25182$

$110$ Public $22087$

$111$ Public $26994$

$112$ Public $21180$

$113$ Public $25349$

$114$ Public $20978$

$115$ Public $25844$

$116$ Public $25448$

$117$ Public $21660$

$118$ Public $17461$

$119$ Public $14929$

$120$ Public $26006$

$121$ Public $21678$

$122$ Public $27400$

$123$ Public $20628$

$124$ Public $30270$

$125$ Public $30015$

$126$ Public $7915$

$127$ Public $24999$

$128$ Public $22912$

$129$ Public $36994$

$130$ Public $19588$

$131$ Public $24220$

$132$ Public $21174$

$133$ Public $25334$

$134$ Public $27711$

$135$ Public $23592$

$136$ Public $28873$

$137$ Public $20611$

$138$ Public $26091$

$139$ Public $34101$

$140$ Public $22300$

$141$ Public $38045$

$142$ Public $24276$

$143$ Public $28170$

$144$ Public $35972$

$145$ Public $22401$

$146$ Public $31958$

$147$ Public $25605$

$148$ Public $28517$

$149$ Public $24272$

$150$ Public $22580$

$151$ Public $21824$

$152$ Public $16077$

$153$ Public $26060$

$154$ Public $27255$

$155$ Public $27681$

$156$ Public $24768$

$157$ Public $19500$

$158$ Public $27006$

$159$ Public $20100$