library(tidyverse)
library(broom)
library(car)
library(effectsize)
library(knitr)
library(kableExtra)
# Create the fertilizer dataset
fertilizer_data <- data.frame(
  yield = c(4.2, 4.5, 4.1, 4.8, 4.3,  # Fertilizer A
            5.1, 5.3, 4.9, 5.2, 5.0,  # Fertilizer B
            3.8, 4.0, 3.6, 4.2, 3.9,  # Fertilizer C
            5.5, 5.8, 5.4, 5.7, 5.6), # Fertilizer D
  fertilizer = factor(rep(c("A", "B", "C", "D"), each = 5))
)

kable(fertilizer_data, caption = "Tomato Yield Data") %>%
  kable_styling(bootstrap_options = c("striped", "hover"))
Tomato Yield Data
yield fertilizer
4.2 A
4.5 A
4.1 A
4.8 A
4.3 A
5.1 B
5.3 B
4.9 B
5.2 B
5.0 B
3.8 C
4.0 C
3.6 C
4.2 C
3.9 C
5.5 D
5.8 D
5.4 D
5.7 D
5.6 D 
fertilizer_data %>%
  group_by(fertilizer) %>%
  summarise(
    mean = mean(yield),
    sd = sd(yield),
    n = n()
  )

Question 1

a)

ggplot(fertilizer_data, aes(x = fertilizer, y = yield)) +
  geom_boxplot(fill = "lightblue") +
  geom_jitter(width = 0.1) +
  labs(title = "Tomato Yield by Fertilizer",
       y = "Yield (kg)",
       x = "Fertilizer")

Analysis:

  • Fertilizer D appears to produce the highest yields.

  • Fertilizer C appears lowest.

  • Variability is similar across groups.

b)

fertilizer_aov <- aov(yield ~ fertilizer, data = fertilizer_data)
summary(fertilizer_aov)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## fertilizer   3  8.522  2.8405   64.19 3.86e-09 ***
## Residuals   16  0.708  0.0443                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

p-value < 0.05, reject H_0. There is a statistically significant difference in mean yield among fertilizers

Question 2

a)

teaching_data <- tibble(
  score = c(78,82,75,80,77,83,79,
            85,88,84,87,86,90,83,
            81,79,83,85,82,78,80),
  method = factor(rep(c("Traditional", "Interactive", "Online"), each = 7))
)

b)

teaching_aov <- aov(score ~ method, data = teaching_data)
summary(teaching_aov)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## method       2  182.0   91.00   14.05 0.000211 ***
## Residuals   18  116.6    6.48                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

p-value < 0.05, reject H_0, significant differences exist.

Question 3

supplier_data <- tibble(
  strength = c(245,250,248,252,249,247,
               240,238,242,241,239,243,
               255,258,254,257,256,253,
               248,246,250,249,247,251),
  supplier = factor(rep(paste("Supplier", 1:4), each = 6))
)

supplier_aov <- aov(strength ~ supplier, data = supplier_data)
summary(supplier_aov)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## supplier     3  676.5   225.5      55 7.66e-10 ***
## Residuals   20   82.0     4.1                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

p-value < 0.01, reject H_0, significant differences exist