wt_before <- c(91, 95, 81, 83, 76, 88, 89, 97, 88, 92)
wt_after <- c(79, 101, 85, 88, 81, 92, 90, 99, 97, 87)

diffs <- wt_after - wt_before


binom.test(sum(diffs > 0), length(diffs))
## 
##  Exact binomial test
## 
## data:  sum(diffs > 0) and length(diffs)
## number of successes = 8, number of trials = 10, p-value = 0.1094
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.4439045 0.9747893
## sample estimates:
## probability of success 
##                    0.8

the p-value os greater than the significance level 0.05 . thus we do not reject the null hypothesis

sample_data <- c(-0.465, 0.120, -0.238, -0.016, 0.417, 0.056, 0.561)

wilcox.test(sample_data, mu = -1.0, alternative = "greater")
## 
##  Wilcoxon signed rank exact test
## 
## data:  sample_data
## V = 28, p-value = 0.007813
## alternative hypothesis: true location is greater than -1

Here the p-value is less than 0.05. Thus we reject the null hypothesis

without_music<-c(3,4,9,10)
with_music<-c(1,2,5,7,8)

wilcox.test(with_music,without_music,alternative="less")
## 
##  Wilcoxon rank sum exact test
## 
## data:  with_music and without_music
## W = 6, p-value = 0.2063
## alternative hypothesis: true location shift is less than 0

Here the p value is less than 0.05. Thus reject the null hypothesis

data<-c(0.0123,0.1039,0.1954,0.2621,0.2802,0.3217,0.3645,0.3919,0.4240,0.4814,0.5139,0.5846,0.6275,0.6541,0.6889,0.7621,0.8020,0.8871,0.9249,0.9634)
sqrt_data<-sqrt(data)
result4<-ks.test(sqrt_data,"punif",min=0,max=1)
result4
## 
##  Exact one-sample Kolmogorov-Smirnov test
## 
## data:  sqrt_data
## D = 0.36196, p-value = 0.007456
## alternative hypothesis: two-sided

Here the p-value is less than the significance level . So we reject the null hypothesis.

tea<-c("A","B","C","D","E","F","G","H","I")
Judge1<-c(1,5,9,7,4,6,8,2,3)
Judge2<-c(4,3,6,8,2,7,9,1,5)

result5<-cor.test(Judge1,Judge2,method="spearman")
result5
## 
##  Spearman's rank correlation rho
## 
## data:  Judge1 and Judge2
## S = 34, p-value = 0.03687
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.7166667

p-value is less than the significance level of 0.05, we reject the null hypothesis of independence.

x<-c(4,6,8,10,12,13,14,15,19)
y<-c(1,2,3,5,7,9,11,18)

result6<-wilcox.test(x,y)
result6
## 
##  Wilcoxon rank sum exact test
## 
## data:  x and y
## W = 54, p-value = 0.09272
## alternative hypothesis: true location shift is not equal to 0

p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis that the two populations are identical.