Paired Samples t-test - to compare before and after or with and without treatment kind of situation data

Suppose we are interested in whether a drug reduces the level of bad cholesterol significantly. We measure cholesterol before and after treatment.

#dataset
before <- c(155, 151, 80, 112, 179, 170, 131, 175, 153, 175)
after <- c(139, 93, 133, 150, 135, 160, 155, 82, 84, 137)

summary(before)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    80.0   136.0   154.0   148.1   173.8   179.0
summary(after)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    82.0   103.0   136.0   126.8   147.2   160.0
sd(before)
## [1] 31.96335
sd(after)
## [1] 29.39312
#converting datasets into data.frame
data <- data.frame(before, after)
data
##    before after
## 1     155   139
## 2     151    93
## 3      80   133
## 4     112   150
## 5     179   135
## 6     170   160
## 7     131   155
## 8     175    82
## 9     153    84
## 10    175   137
summary(data)
##      before          after      
##  Min.   : 80.0   Min.   : 82.0  
##  1st Qu.:136.0   1st Qu.:103.0  
##  Median :154.0   Median :136.0  
##  Mean   :148.1   Mean   :126.8  
##  3rd Qu.:173.8   3rd Qu.:147.2  
##  Max.   :179.0   Max.   :160.0
res <- t.test(before, after, paired = TRUE, alternative = "two.sided")
res
## 
##  Paired t-test
## 
## data:  before and after
## t = 1.401, df = 9, p-value = 0.1947
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -13.09182  55.69182
## sample estimates:
## mean of the differences 
##                    21.3
#Two sided Paired Sample T Test shows that there is no significant difference between before and after as p-value > 0.05 fails to reject the null

res2 <- t.test(before, after, paired = TRUE, alternative = "less")
res2
## 
##  Paired t-test
## 
## data:  before and after
## t = 1.401, df = 9, p-value = 0.9026
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
##      -Inf 49.16901
## sample estimates:
## mean of the differences 
##                    21.3
res3 <- t.test(before, after, paired = TRUE, alternative = "greater")
res3
## 
##  Paired t-test
## 
## data:  before and after
## t = 1.401, df = 9, p-value = 0.09737
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  -6.569011       Inf
## sample estimates:
## mean of the differences 
##                    21.3