Lab Name

#install.packages("BSDA")
library(tidyverse)

## Warning: package 'tidyverse' was built under R version 4.0.2

## Warning: package 'tibble' was built under R version 4.0.2

## Warning: package 'tidyr' was built under R version 4.0.2

## Warning: package 'dplyr' was built under R version 4.0.2

library(openintro)

## Warning: package 'openintro' was built under R version 4.0.2

## Warning: package 'airports' was built under R version 4.0.2

## Warning: package 'cherryblossom' was built under R version 4.0.2

## Warning: package 'usdata' was built under R version 4.0.2

library(BSDA)

## Warning: package 'BSDA' was built under R version 4.0.3

getwd()

## [1] "C:/Users/Jerome/Documents/201030_Math217_Week8_HW"

Problem 7.2.5

tsum.test(18.3, 17.8,33, 13.9,19.1, 51)

## 
##  Welch Modified Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 1.075, df = 71.901, p-value = 0.286
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.759852 12.559852
## sample estimates:
## mean of x mean of y 
##      18.3      13.9

Problem 7.5.5

tsum.test (972.1, 245.1, 12, 843.4, 251.2, 15)

## 
##  Welch Modified Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 1.3408, df = 23.961, p-value = 0.1925
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -69.41849 326.81849
## sample estimates:
## mean of x mean of y 
##     972.1     843.4

tsum.test (972.1, 245.1, 12, 843.4, 251.2, 15, conf.level = 0.9)

## 
##  Welch Modified Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 1.3408, df = 23.961, p-value = 0.1925
## alternative hypothesis: true difference in means is not equal to 0
## 90 percent confidence interval:
##  -35.52815 292.92815
## sample estimates:
## mean of x mean of y 
##     972.1     843.4

Practice t-test

library(infer)

## Warning: package 'infer' was built under R version 4.0.2

a <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110)
b <- c(5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105)

mean(a)

## [1] 60

sd(b)

## [1] 33.16625

mean(b)

## [1] 55

sd(a)

## [1] 33.16625

t.test(a,b, alternative = "less")

## 
##  Welch Two Sample t-test
## 
## data:  a and b
## t = 0.35355, df = 20, p-value = 0.6363
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
##     -Inf 29.3912
## sample estimates:
## mean of x mean of y 
##        60        55

data(yrbss)
class(yrbss$height)

## [1] "numeric"

class(yrbss$weight)

## [1] "numeric"

t.test(yrbss$height,yrbss$weight, alternative = "greater")

## 
##  Welch Two Sample t-test
## 
## data:  yrbss$height and yrbss$weight
## t = -439.47, df = 12579, p-value = 1
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  -66.46311       Inf
## sample estimates:
## mean of x mean of y 
##  1.691241 67.906503

Problem 7.5.10

tsum.test(31.96,    12.05, 25, 25.32, 13.78, 25, alternative = "less")

## 
##  Welch Modified Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 1.8137, df = 47.161, p-value = 0.962
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
##        NA 12.78263
## sample estimates:
## mean of x mean of y 
##     31.96     25.32

tsum.test(31.96,    12.05, 25, 25.32, 13.78, 25, alternative = "greater")

## 
##  Welch Modified Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 1.8137, df = 47.161, p-value = 0.03805
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  0.4973688        NA
## sample estimates:
## mean of x mean of y 
##     31.96     25.32

tsum.test(31.96,    12.05, 25, 25.32, 13.78, 25)

## 
##  Welch Modified Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 1.8137, df = 47.161, p-value = 0.0761
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.7245135 14.0045135
## sample estimates:
## mean of x mean of y 
##     31.96     25.32

Problem 7.6.7

tsum.test (0.354, 0.058, 530, 0.263, 0.051, 420)

## 
##  Welch Modified Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 25.698, df = 937.77, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.08405043 0.09794957
## sample estimates:
## mean of x mean of y 
##     0.354     0.263

Problem 7.10.3

toluene <- c(3420, 2314, 1911, 2464, 2781, 2803)
control <- c(1820, 1843, 1397, 1803, 2539, 1990)

wilcox.test(toluene, control, alternative = "two.sided", conf.int = TRUE, conf.level= 0.95)

## 
##  Wilcoxon rank sum exact test
## 
## data:  toluene and control
## W = 32, p-value = 0.02597
## alternative hypothesis: true location shift is not equal to 0
## 95 percent confidence interval:
##    91 1406
## sample estimates:
## difference in location 
##                    726

wilcox.test(toluene, control, alternative = "greater", conf.int = TRUE, conf.level= 0.95)

## 
##  Wilcoxon rank sum exact test
## 
## data:  toluene and control
## W = 32, p-value = 0.01299
## alternative hypothesis: true location shift is greater than 0
## 95 percent confidence interval:
##  242 Inf
## sample estimates:
## difference in location 
##                    726

Problem 7.10.7

single <- c(3.3, 2.4, 2.5, 3.3, 2.4)
group <- c(3.9, 4.1, 4.8, 3.9, 3.4)
wilcox.test(single, group, alternative = "two.sided", conf.int = TRUE, conf.level= 0.95)

## Warning in wilcox.test.default(single, group, alternative = "two.sided", :
## cannot compute exact p-value with ties

## Warning in wilcox.test.default(single, group, alternative = "two.sided", :
## cannot compute exact confidence intervals with ties

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  single and group
## W = 0, p-value = 0.01141
## alternative hypothesis: true location shift is not equal to 0
## 95 percent confidence interval:
##  -2.2999860 -0.5999636
## sample estimates:
## difference in location 
##              -1.400047