index

library(tidyverse)

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library(mosaic)

Registered S3 method overwritten by 'mosaic':
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  fortify.SpatialPolygonsDataFrame ggplot2

The 'mosaic' package masks several functions from core packages in order to add 
additional features.  The original behavior of these functions should not be affected by this.

Attaching package: 'mosaic'

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    quantile, sd, t.test, var

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library(ggformula)
library(infer)

Attaching package: 'infer'

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library(broom) # Clean test results in tibble form
library(resampledata) # Datasets from Chihara and Hesterberg's book

Attaching package: 'resampledata'

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library(openintro) # More datasets

Loading required package: airports
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Loading required package: usdata

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set.seed(40)  # for replication
# Data as individual vectors ( for t.tests etc)
y <- rnorm(50, mean = 2, sd = 2)

# And as tibble too
mydata <- tibble(y = y)
mydata

# A tibble: 50 × 1
        y
    <dbl>
 1  2.96 
 2  2.99 
 3  0.281
 4  0.342
 5  1.36 
 6 -0.608
 7 -0.843
 8  5.49 
 9  1.42 
10 -0.618
# ℹ 40 more rows

##tibble- dataframe

##y <- rnorm- generate 50 random numbers

##so we have vector(array?) y with 50 normally distributed random numbers - data is symetrically distribted around the mean

mydata %>%
    gf_density(~y) %>% ##distribution of y values 
    gf_fitdistr(dist = "dnorm") %>% ##normal distribution based on mean and sd? always a symmetrical bell curve 
    gf_labs(title = "Densities of Original Data Variables", subtitle = "Compared with Normal Density")

# t-test
t1 <- mosaic::t_test(
          y, # Name of variable
          mu = 0, # belief of population mean
          alternative = "two.sided") %>% # Check both sides
  
  broom::tidy() # Make results presentable, and plottable!!
t1

# A tibble: 1 × 8
  estimate statistic     p.value parameter conf.low conf.high method alternative
     <dbl>     <dbl>       <dbl>     <dbl>    <dbl>     <dbl> <chr>  <chr>      
1     2.05      6.79     1.43e-8        49     1.44      2.65 One S… two.sided  

mean_belief_pop <- 0  # Assert our belief
# Sample Mean
mean_y <- mean(y)
mean_y

[1] 2.045689

## Sample standard error
std_error <- sd(y)/sqrt(length(y))
std_error

[1] 0.3014752

## Confidence Interval of Observed Mean
conf_int <- tibble(ci_low = mean_y - 1.96 * std_error, ci_high = mean_y + 1.96 *
    std_error)
conf_int

# A tibble: 1 × 2
  ci_low ci_high
   <dbl>   <dbl>
1   1.45    2.64

## Difference between actual and believed mean
mean_diff <- mean_y - mean_belief_pop
mean_diff

[1] 2.045689

## Test Statistic
t <- mean_diff/std_error
t

[1] 6.785596

##sample mean is 2.04, likelihood of zero being the mean is very low

#p value, t-test

##based on the assumption that our sample is a bell curve

##permutation