Q.Explain the flaws in the following analysis or conclusion.(Note that this is not about chi-squared test per se, perhaps, itis about what a statistical analysis (hypothesis testing in thiscase) can tell us and what it cannot) Background - The ScholarshipCommittee comprises 3 faculty members, one of whom is Professor X.Professor X also wrote recommendation letter for 5 students whotook his class earlier and four of them were awarded scholarships(out of a total of six scholarships awarded to graduate students).A student who applied but was not awarded a scholarship accusedProfessor X of favoritism, claiming that he/she was denied ascholarship despite having a very high GPA because he/she did nottake class under Professor X and had declined him/her arecommendation letter. The student then did following statisticalanalysis as an evidence of favoritism . The student runs aChisq-test and his result shows not independent between studentswho took class under Professor X and Students got scholarship. H0:students who get scholarship is independent with whether they havetaken class under Professor X H1: not independent # Let totalnumber of students who applied for scholarship is 70, and only 5people get the scholarship, conservatively estimate only 3 out of 5students took Class with ProfessorX, the other two selected did nottake Class with ProfessorX # chisquare test shows the p-value<0.05, thus we reject H0 at .05 level and conclude students whogot scholarship was affected by whether they have class underProfessor X #student in addition tests , how about the totalapplicants were 60, or 80? and find out either case we reject H0,they are not independent.