Problem 1:
data("UCBAdmissions",package="datasets")
View(UCBAdmissions)
## Warning in system2("/usr/bin/otool", c("-L", shQuote(DSO)), stdout = TRUE):
## running command ''/usr/bin/otool' -L '/Library/Frameworks/R.framework/
## Resources/modules/R_de.so'' had status 1
(a) Find the total number of cases contained in this table
sum(UCBAdmissions)
## [1] 4526
(b) For each department, find the total number of applicants.
margin.table(UCBAdmissions,margin=3)
## Dept
## A B C D E F
## 933 585 918 792 584 714
(c) For each department, find the overall proportion of applicants who were admitted.
prop.table(margin.table(UCBAdmissions,c(1,3)))
## Dept
## Admit A B C D E
## Admitted 0.13278833 0.08174989 0.07114450 0.05943438 0.03247901
## Rejected 0.07335395 0.04750331 0.13168361 0.11555457 0.09655325
## Dept
## Admit F
## Admitted 0.01016350
## Rejected 0.14759169
(d) Construct a tabular display of department (rows) and gender (columns), showing the proportion of applicants in each cell who were admitted relative to the total applicants in that cell.
ftable(prop.table(UCBAdmissions,c(2,3)),2)
## Dept A B C D E F
## Admit Gender
## Admitted Male 0.62060606 0.63035714 0.36923077 0.33093525 0.27748691 0.05898123
## Female 0.82407407 0.68000000 0.34064081 0.34933333 0.23918575 0.07038123
## Rejected Male 0.37939394 0.36964286 0.63076923 0.66906475 0.72251309 0.94101877
## Female 0.17592593 0.32000000 0.65935919 0.65066667 0.76081425 0.92961877
Problem 2:
data("UKSoccer",package="vcd")
ftable(UKSoccer)
## Away 0 1 2 3 4
## Home
## 0 27 29 10 8 2
## 1 59 53 14 12 4
## 2 28 32 14 12 4
## 3 19 14 7 4 1
## 4 7 8 10 2 0
(a) Verify that the total number of games represented in this table is 380.
sum(UKSoccer)
## [1] 380
(b)Find the marginal total of the number of goals scored by each of the home and away teams.
addmargins(UKSoccer)
## Away
## Home 0 1 2 3 4 Sum
## 0 27 29 10 8 2 76
## 1 59 53 14 12 4 142
## 2 28 32 14 12 4 90
## 3 19 14 7 4 1 45
## 4 7 8 10 2 0 27
## Sum 140 136 55 38 11 380
(c) Express each of the marginal totals as proportions.
prop.table(addmargins(UKSoccer))
## Away
## Home 0 1 2 3 4
## 0 0.0177631579 0.0190789474 0.0065789474 0.0052631579 0.0013157895
## 1 0.0388157895 0.0348684211 0.0092105263 0.0078947368 0.0026315789
## 2 0.0184210526 0.0210526316 0.0092105263 0.0078947368 0.0026315789
## 3 0.0125000000 0.0092105263 0.0046052632 0.0026315789 0.0006578947
## 4 0.0046052632 0.0052631579 0.0065789474 0.0013157895 0.0000000000
## Sum 0.0921052632 0.0894736842 0.0361842105 0.0250000000 0.0072368421
## Away
## Home Sum
## 0 0.0500000000
## 1 0.0934210526
## 2 0.0592105263
## 3 0.0296052632
## 4 0.0177631579
## Sum 0.2500000000