Muhammad Bilal Ds-5th(5121107)(Comparing Proportions in R)

##One-proportion z-Test: #Compute one proportion z-test in R

res <- prop.test(x = 95, n = 160, p = 0.5, 
                 correct = FALSE)
# Printing the results
res

## 
##  1-sample proportions test without continuity correction
## 
## data:  95 out of 160, null probability 0.5
## X-squared = 5.625, df = 1, p-value = 0.01771
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.5163169 0.6667870
## sample estimates:
##       p 
## 0.59375

# printing the p-value
res$p.value

## [1] 0.01770607

# printing the mean
res$estimate

##       p 
## 0.59375

# printing the confidence interval
res$conf.int

## [1] 0.5163169 0.6667870
## attr(,"conf.level")
## [1] 0.95

##Two-proportions z-Test #Compute two-proportions z-test in R:

res <- prop.test(x = c(490, 400), n = c(500, 500))
# Printing the results
res 

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(490, 400) out of c(500, 500)
## X-squared = 80.909, df = 1, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  0.1408536 0.2191464
## sample estimates:
## prop 1 prop 2 
##   0.98   0.80

# printing the p-value
res$p.value

## [1] 2.363439e-19

# printing the mean
res$estimate

## prop 1 prop 2 
##   0.98   0.80

# printing the confidence interval
res$conf.int

## [1] 0.1408536 0.2191464
## attr(,"conf.level")
## [1] 0.95

##Chi-square goodness of fit test in R:

tulip <- c(81, 50, 27)
res <- chisq.test(tulip, p = c(1/3, 1/3, 1/3))
res

## 
##  Chi-squared test for given probabilities
## 
## data:  tulip
## X-squared = 27.886, df = 2, p-value = 8.803e-07

# Access to the expected values
res$expected

## [1] 52.66667 52.66667 52.66667

#comparing observed to expected proportions

tulip <- c(81, 50, 27)
res <- chisq.test(tulip, p = c(1/2, 1/3, 1/6))
res

## 
##  Chi-squared test for given probabilities
## 
## data:  tulip
## X-squared = 0.20253, df = 2, p-value = 0.9037

# printing the p-value
res$p.value

## [1] 0.9036928

# printing the mean
res$estimate

## NULL