Assignment 2

Hypothesis Testing

宋春林

Group 2; ID: 201328006310005

Data

问题：已知A地家蝇翅膀长度均值47mm，为研究B地家蝇翅膀长度和A地有无差异，随机抽取B地100只家蝇，测量其翅膀长度。

H0假设：μ=47，即B地家蝇翅膀长度与A地一致

Ha假设：μ≠47，即B地家蝇翅膀长度与A地不一致

α=0.05

R Script

data <- read.csv("Wing.csv")
l <- data$wl
l

##   [1] 36 37 38 38 39 39 40 40 40 40 41 41 41 41 41 41 42 42 42 42 42 42 42
##  [24] 43 43 43 43 43 43 43 43 44 44 44 44 44 44 44 44 44 45 45 45 45 45 45
##  [47] 45 45 45 45 46 46 46 46 46 46 46 46 46 46 47 47 47 47 47 47 47 47 47
##  [70] 48 48 48 48 48 48 48 48 49 49 49 49 49 49 49 50 50 50 50 50 50 51 51
##  [93] 51 51 52 52 53 53 54 55

mean(l)

## [1] 45.5

sd(l)

## [1] 3.92

shapiro.test(l)

## 
##  Shapiro-Wilk normality test
## 
## data:  l
## W = 0.9928, p-value = 0.8761

qqnorm(l)

hist(l)

quantile(l)

##   0%  25%  50%  75% 100% 
## 36.0 43.0 45.5 48.0 55.0

t.test(l, mu = 47, var.equal = FALSE, alternative = c("two.sided"))

## 
##  One Sample t-test
## 
## data:  l
## t = -3.827, df = 99, p-value = 0.0002274
## alternative hypothesis: true mean is not equal to 47
## 95 percent confidence interval:
##  44.72 46.28
## sample estimates:
## mean of x 
##      45.5

Conclusion Statement

基于100个样本的p-value = 0.0002274 < 0.05，因此有充足的理由拒绝H0假设，即B地家蝇翅膀长度与A地不一致，并且有超过95%的把握确信B地家蝇翅膀长度比A地短。