Assignment 5, Question 1

Is there difference between the current distribution of ice cream purchases versus the expected distribution (20% chocolate, 20% strawberry, 20% mango, 40% vanilla)?

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(rmarkdown)
A5Q1_1 <- read_excel("~/Documents/Documents - Marshall’s MacBook Pro/Education/SLU/2026/AA 5221/Data/Week 5 data/A5Q1-1.xlsx")
observed <- table(A5Q1_1$flavor)
observed

## 
##  Chocolate      Mango Strawberry    Vanilla 
##         87         32         57         74

barplot(observed,
        main="Ice Cream Purchases",
        xlab="Flavor",
        ylab="Count",
        col = rainbow(length(observed)))

expected <- c(.2, .2, .2, .4)
chi_result <- chisq.test(x = observed, p = expected)
chi_result

## 
##  Chi-squared test for given probabilities
## 
## data:  observed
## X-squared = 41.6, df = 3, p-value = 4.878e-09

w <- sqrt(as.numeric(chi_result$statistic) / sum(observed))
w

## [1] 0.4079216

A Chi-Square Goodness of Fit test was conducted to determine if there was a difference between the observed [Ice Cream Flavor] frequencies and the expected frequencies.

The results showed that there was a difference between the observed and expected frequencies, χ²(3) = 41.6, p < .001.

The difference was moderate, (Cohen’s W = .41).