1. Hypothesis Testing is a form of statistical analysis where you have an assumption you wish to test
2. The goal of Hypothesis Testing is to determine if there is enough evidence to support or reject the claim you made in you Hypothesis
3. It is used to determine the relationship between two variables

1. State the Null Hypothesis (H0)
2. State the Alternative Hypothesis (H1 or Ha)
3. Set 𝜶 (Significane Level)
4. Collect Data
5. Select and Calcuate a Test Statistic
6. Construct Acceptance and Rejection Regions
7. Draw Conclusion about H0

μ is the population mean and μ0 is the hypothetical population mean \[ \\H_0: \mu = \mu_0 \\ H_a: \mu \neq \mu_0 \]

1. Z Test

• Used to determine if a relationship is staistically significant

1. T Test

• Used to compare the means of two groups

1. Chi-Square

• Used to determine if your data is as predicted (oberserved values compared to predicted values)

1. ANOVA

• Used to compare the means of three or more groups

\[ Z = \frac{\bar{X} - \mu_0}{\sigma / \sqrt{n}} \\ \]

\[ t = \frac{\bar{X} - \mu}{S / \sqrt{n}} \\ \]

\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]

df1 = 5  
df2 = 20 
x_vals= seq(0, 5, length.out = 100) 
y_vals = df(x_vals, df1, df2) 
f_data= data.frame(F_stat = x_vals, Density = y_vals)
alpha=  0.05
F_critical = qf(1 - alpha, df1, df2)
ggplot(f_data, aes(x = F_stat, y = Density)) +
  geom_line(color = "black", linewidth = 1) +  
  geom_ribbon(aes(ymax = ifelse(F_stat >= F_critical, Density, NA),
  ymin = 0), fill = "red", alpha = 0.5) + annotate("text", 
  x = F_critical - 0.5, y = 0.1, label = "Accept H0", 
  color = "green", size = 5) + annotate("text", 
  x = F_critical + 0.3, y = 0.05, 
  label = "Reject H0", color = "red", size = 5) +
  labs(title = "F-Distribution Hypothesis Test",
       x = "F Statistic", y = "P(F)")