• In statistics, hypothesis testing is a form of analysis in which you test your assumptions about a specific parameter.
• A statistical analyst will validate these assumptions through collection and evaluating a data set.
• The two forms of hypotheses used to put these theories to the test are null and alternative hypotheses.
• Null hypothesis: The claim being made that the researcher is attempting to disprove.
• Alternative hypothesis: The hypothesis the researcher is attempting to prove through data and research.

• State your prediction using both a null and alternative hypothesis.
  
  Example:
  
• Null Hypothesis: On average, men are not taller than women.
  
• Alternative Hypothesis: On average, men are taller than women.
  

• Test your hypothesis by collecting data related to your hypotheses, considering the scope and various control variables that could affect your data collection.
  
  Example:
  
• Collect data on heights of men and women on a global scale, looking into research and census information.

• Doing a statistical test will check if the observed data is consistent with the proposed hypothesis.
• Some statistical tests that are frequently used include a T-test, Z-test, Chi-square test, and Analysis of Variance.
  
• A T-test is calculated as follows:
  \[ t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}} \] Example:
  
• Performing a t-test to check the heights of men and women would compare the means of the two different groups.
  
• This results in an average height of 175.4cm for men and 161.7cm for women, as well as a p-value of 0.002 declaring the likelihood of this difference if the null hypothesis is true.

• Compare the p-value to the significance level (\(\alpha\))
• If \(p \leq \alpha\), reject the null hypothesis.
• If \(p > \alpha\), accept the null hypothesis.

• Present your findings to your peers in a research paper or other form of presentation.
  
• Here is a violin ggplot showing our findings regarding height in men VS women:

male_heights <- rnorm(100, mean = 175.4, sd = 7)
female_heights <- rnorm(100, mean = 161.74, sd = 6)
height_data <- data.frame(
  height = c(male_heights, female_heights),
  gender = factor(rep(c("Men", "Women"), each = 100))
)
ggplot(height_data, aes(x = gender, y = height, fill = gender)) + 
  geom_violin(trim = F, alpha = 0.6) + 
  stat_summary(fun = mean, geom = "point", shape = 23, size = 1,
               color = "black", fill = "white") +
  labs(title = "Findings of Average Height by Gender",
       x = "Gender", y = "Height in Centimeters") +
  scale_fill_manual(values = c("blue", "pink")) +
  theme_minimal()