Inference_Week4_RLAB

getwd()

## [1] "C:/Users/Jerome/Documents/0000_Work_Files/0000_Coursera/Statistics_with_R_Specialization/Course_2_Inferential_Stats/Week4"

library(statsr)

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

library(dplyr)

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

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(ggplot2)
library(tables)

## Warning: package 'tables' was built under R version 4.0.5

data(atheism)

 write.csv (atheism, file = "atheism.csv", row.names = FALSE)
 atheism <- read.csv("atheism.csv", header = TRUE)

us12 <- atheism %>%
  filter(nationality == "United States" , atheism$year == "2012")

write.csv (us12, file = "us12.csv", row.names = FALSE)
us12 <- read.csv("us12.csv", header = TRUE)

table (us12$response)

## 
##     atheist non-atheist 
##          50         952

data("atheism")
library("dplyr")
us12 <- atheism %>%
        filter(nationality == "United States" , atheism$year == "2012")
inference(y = response, data = us12, statistic = "proportion",
          type = "ci",
          method = "theoretical", 
          success = "atheist")

## Single categorical variable, success: atheist
## n = 1002, p-hat = 0.0499
## 95% CI: (0.0364 , 0.0634)

inference(y = response, data = us12, statistic = "proportion", type = "ci", method = "theoretical", success = "atheist")

## Single categorical variable, success: atheist
## n = 1002, p-hat = 0.0499
## 95% CI: (0.0364 , 0.0634)

france12 <- atheism %>%
  filter(nationality == "France" , atheism$year == "2012")

china12 <- atheism %>%
  filter(nationality == "China" , atheism$year == "2012")

### ME and p

d <- data.frame(p <- seq(0, 1, 0.01))
n <- 1000
d <- d %>%
  mutate(me = 1.96*sqrt(p*(1 - p)/n))
ggplot(d, aes(x = p, y = me)) +
  geom_line()

spain <- atheism %>%
  filter(nationality == "Spain")

write.csv (spain, file = "spain.csv", row.names = FALSE)
spain <- read.csv("spain.csv", header = TRUE)

table(spain$year)

## 
## 2005 2012 
## 1146 1145

prop.test(table(spain$year), correct=FALSE) 

## 
##  1-sample proportions test without continuity correction
## 
## data:  table(spain$year), null probability 0.5
## X-squared = 0.00043649, df = 1, p-value = 0.9833
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.4797609 0.5206749
## sample estimates:
##         p 
## 0.5002182

us_both <- atheism %>%
  filter(nationality == "United States" )

write.csv (us_both, file = "us_both.csv", row.names = FALSE)
us_both <- read.csv("us_both.csv", header = TRUE)

table(us_both$year)

## 
## 2005 2012 
## 1002 1002

prop.test(table(us_both$year), correct=FALSE) 

## 
##  1-sample proportions test without continuity correction
## 
## data:  table(us_both$year), null probability 0.5
## X-squared = 0, df = 1, p-value = 1
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.4781298 0.5218702
## sample estimates:
##   p 
## 0.5