Yes, random sampling is employed in the study described.
Yes, it would be fair because it is a random sample which is averaged over the amount of people sampled. The final answer may vary considering the amount of people applied, however the average should be very similar.
4,526 people applied for UC Berkeley.
1,835 women applied for UC Berkeley.
## 'data.frame': 4526 obs. of 3 variables:
## $ Admit : Factor w/ 2 levels "Admitted","Rejected": 1 1 1 1 1 1 1 1 1 1 ...
## $ Gender: Factor w/ 2 levels "Female","Male": 2 2 2 2 2 2 2 2 2 2 ...
## $ Dept : Factor w/ 6 levels "A","B","C","D",..: 1 1 1 1 1 1 1 1 1 1 ...## Admit Gender Dept
## Admitted:1755 Female:1835 A:933
## Rejected:2771 Male :2691 B:585
## C:918
## D:792
## E:584
## F:714## Admit Gender Dept
## 1 Admitted Male A
## 2 Admitted Male A
## 3 Admitted Male A
## 4 Admitted Male A
## 5 Admitted Male A
## 6 Admitted Male A108 women applied for department A
## # A tibble: 12 x 3
## Dept Gender n
## <fct> <fct> <int>
## 1 A Female 108
## 2 A Male 825
## 3 B Female 25
## 4 B Male 560
## 5 C Female 593
## 6 C Male 325
## 7 D Female 375
## 8 D Male 417
## 9 E Female 393
## 10 E Male 191
## 11 F Female 341
## 12 F Male 373Approximately 29 percent of women who applied, were accepted, thismeans 71 percent were rejected.
## # A tibble: 2 x 4
## # Groups: Gender [2]
## Gender Admit n prop
## <fct> <fct> <int> <dbl>
## 1 Female Admitted 557 0.304
## 2 Male Admitted 1198 0.445This is a random sampling method. There is no selection of the people being used for their criteria, it is entirely random.