# ==============================================================================
# SweetCelebration.r
# A Sweet Celebration: Sampling Distributions
# academy.statypus.org
# ==============================================================================

# Instructions: Execute each line one by one as directed by your PDF worksheet.
# Inspect the objects created in your Environment pane.

# --- Part 1: Macro Population Audit ---

# Download the audit dataset directly from the Statypus servers.
candy_data <- read.csv("https://statypus.org/files/candy_data.csv")

# Look at your Environment pane. Click the spreadsheet icon next to candy_data 
# to see the structure of the bag_id, white_count, and blue_count columns.

# Task: Use the sum() function to calculate the total candies across all 100 bags.
total_white <- sum(candy_data$white_count)
total_blue  <- sum(candy_data$blue_count)

total_white
total_blue


# --- Part 2: Manual Row Extraction ---

# R allows us to isolate specific rows in a column using the bracket [ ] operator.
# Let's extract the white and blue counts for the very first bag:
candy_data$white_count[1]
candy_data$blue_count[1]

# We can manually calculate the proportion for Bag 1 using R as a calculator:
candy_data$white_count[1] / (candy_data$white_count[1] + candy_data$blue_count[1])

# Task: Modify the brackets below to find the counts and calculate the 
# proportion for Bag 3, then record it on your worksheet.
candy_data$white_count[3] 
candy_data$blue_count[3]
# Type your division math here:



# --- Part 3: Vectorization ---

# Let's stop checking them one by one. We will calculate the total candies 
# in each bag for the entire column simultaneously.
candy_data$total_in_bag <- candy_data$white_count + candy_data$blue_count
# Note that this actually expands the data frame by adding a new column 
# called total_in_bag. 

# Now, we divide the entire white column by the total column to generate 100 p-hats.
candy_data$prop_white <- candy_data$white_count / candy_data$total_in_bag
# Again, this extends the data frame by adding a new column called prop_white, 
# which contains the sample proportion of white candies for each bag.

# Visualize the resulting Sampling Distribution of p-hat.
hist(candy_data$prop_white, 
     breaks = 12, 
     col = "lightgray", 
     main = "Sampling Distribution of 100 Guest Experiences (p-hat)",
     xlab = "Sample Proportion of White Candies",
     ylab = "Frequency (Number of Bags)")

# Add a red line marking the location of the very first bag we opened.
abline(v = 31/52, col = "red", lwd = 2, lty = 2)


# --- Part 4: Theoretical Tail Verification ---

# Using the theoretical parameters calculated by hand on Page 5.
theoretical_mean <- 0.50
theoretical_sd   <- sqrt((0.50 * (1 - 0.50)) / 50)

# Task: Use the pnorm function to find the probability of getting 
# a sample proportion (p-hat) of 0.596 or greater.
# Hint: Remember to set lower.tail correctly for a "greater than" question!

pnorm( )

# We can check to see how close our actual data fits this model.
# We can use the sum() function along with a logical condition to count how many
# bags had a p-hat of 0.596 or greater.

sum( candy_data$prop_white >= 0.596 )

# The reason this works is that the line of code inside the sum() function 
# creates a vector of TRUE and FALSE values, and then the sum()
# function treats TRUE as 1 and FALSE as 0, so it effectively counts the TRUEs.