In the fall of 1973, University of California Berkeley student admissions data seemed to show a pattern of bias against female graduate students. In spite of the progressive reputation of the university at the time, the data appeared to indicate that female applicants to the graduate school had much lower rates of admission than men. You will examine the data yourself to determine whether the graduate admissions committees had a bias against women.
Of the 4,526 applicants in this data set, 1,755 were admitted for an overall admission rate of approximately 39%. The admission rate for men was 45%, while the admission rate for women was 30%. Complete the following table.
|
Gender |
Number Admitted |
Number Rejected |
|
Male |
||
|
Female |
Indicate how your numbers are consistent with these given admission rates for men and women. (Round your answers to four decimal places.)
admission rate for menadmission rate for women
Use these data to conduct a test of independence between gender and admission. Use a significance level of 0.05.
State the null and alternative hypotheses.
H 0 : Gender and whether or not an applicant is admitted are dependent.
H 1 : Gender and whether or not an applicant is admitted are not dependent. H 0 : Gender and whether or not an applicant is admitted are not dependent.
H 1 : Gender and whether or not an applicant is admitted are dependent. H 0 : Gender and whether or not an applicant is admitted are not independent.
H 1 : Gender and whether or not an applicant is admitted are independent. H 0 : Gender and whether or not an applicant is admitted are independent.
H 1 : Gender and whether or not an applicant is admitted are not independent.
State the χ 2 statistic, degrees of freedom, and the P -value. (Round your answer for χ 2 to two decimal places and your P -value to three decimal places.)
χ 2
=df= P -value=
Interpret the result with respect to gender bias in admissions.
There is sufficient evidence at a significance level of 0.05 to conclude that there is gender bias in admissions.There is insufficient evidence at a significance level of 0.05 to conclude that there is gender bias in admissions.
Now, let’s reconsider this data by investigating whether there is a relationship between gender and department by conducting a test of independence between gender and department, ignoring admittance. Use a significance level of 0.05.
State the null and alternative hypotheses.
H 0 : Gender and department are not dependent.
H 1 : Gender and department are dependent. H 0 : Gender and department are dependent.
H 1 : Gender and department are not dependent. H 0 : Gender and department are independent.
H 1 : Gender and department are not independent. H 0 : Gender and department are not independent.
H 1 : Gender and department are independent.
State the χ 2 statistic, degrees of freedom, and the P -value. (Round your answer for χ 2 to two decimal places and your P -value to three decimal places.)
χ 2
=df= P -value=
Interpret the result with respect to whether the men and women tend to apply to different departments.
There is sufficient evidence at a significance level of 0.05 to conclude that gender and department are not independent.There is insufficient evidence at a significance level of 0.05 to conclude that gender and department are not independent.
If you conducted a third test of independence between admission and department with the following hypotheses, you would reject the null hypothesis and conclude that gender and department are not independent ( P -value = 0.000).
H 0 :
Admission and department are independent.
H 1 :
Admission and department are not independent.
Specifically, departments A and B admit a greater percentage of students than would be expected if there were no relationship, while departments D, E, and F admit a smaller percentage of students.
In light of these two test results and the following graph, explain why the university is actually not guilty of bias, even though the overall percentage of women admitted is significantly less than the percentage of men admitted.
