2021.1.3 助教練習

a <- c(86, 82, 74, 85, 76, 79, 82, 83, 83, 79, 82)
b <- c(81, 77, 63, 75, 69, 86, 81, 60)
shapiro.test(a)

## 
##  Shapiro-Wilk normality test
## 
## data:  a
## W = 0.93295, p-value = 0.4414

shapiro.test(b)

## 
##  Shapiro-Wilk normality test
## 
## data:  b
## W = 0.94077, p-value = 0.6187

var.test(a,b) 

## 
##  F test to compare two variances
## 
## data:  a and b
## F = 0.15791, num df = 10, denom df = 7, p-value = 0.009825
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.03316711 0.62372643
## sample estimates:
## ratio of variances 
##          0.1579125

t.test(a,b, paired = FALSE, var.equal = FALSE, alternative = "two.sided")

## 
##  Welch Two Sample t-test
## 
## data:  a and b
## t = 2.0356, df = 8.6206, p-value = 0.07366
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.831606 14.831606
## sample estimates:
## mean of x mean of y 
##        81        74

#H0<= 0.11 Ha: > 0.11
binom.test(18, 120, p = 0.11, alternative = "greater" )

## 
##  Exact binomial test
## 
## data:  18 and 120
## number of successes = 18, number of trials = 120, p-value = 0.1079
## alternative hypothesis: true probability of success is greater than 0.11
## 95 percent confidence interval:
##  0.09924886 1.00000000
## sample estimates:
## probability of success 
##                   0.15

#因為p = 0.1079 >0.05, 所以沒有推翻虛無假說，所以失業率沒有高於11%）