Question

Q.Explain the flaws in the following analysis or conclusion. (Note that this is not about chi-squared test per se, perhaps, it is about what a statistical analysis (hypothesis testing in this case) can tell us and what it cannot)

Background - The Scholarship Committee comprises 3 faculty members, one of whom is Professor X. Professor X also wrote recommendation letter for 5 students who took 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 accused Professor X of favoritism, claiming that he/she was denied a scholarship despite having a very high GPA because he/she did not take class under Professor X and had declined him/her a recommendation letter. The student then did following statistical analysis as an evidence of favoritism .

The student runs a Chisq-test and his result shows not independent between students who took class under Professor X and Students got scholarship.

H0: students who get scholarship is independent with whether they have taken class under Professor X

H1: not independent

# Let total number of students who applied for scholarship is 70, and only 5 people get the scholarship, conservatively estimate only
3 out of 5 students took Class with ProfessorX, the other two selected did not take Class with ProfessorX

# chisquare test shows the p-value <0.05, thus we reject H0 at .05 level and conclude students who got scholarship was affected by whether they have class under Professor X

#student in addition tests , how about the total applicants were 60, or 80?
and find out either case we reject H0, they are not independent.

Answer 1