Hypothesis Testing
Conduct hypothesis tests by calculating test statistics and p-values to evaluate null hypotheses. Visualize Type I and Type II errors, significance levels, and the decision-making process for rejecting or failing to reject the null hypothesis based on sample evidence.
Scatter Plot & Correlation
Create scatter plots to visualize bivariate relationships and calculate correlation coefficient $r$ to measure linear association strength. Explore how outliers, direction, form, and strength affect correlation, and understand why correlation does not imply causation.
Least Squares Regression Line
Calculate the least squares regression line $hat{y} = a + bx$ that minimizes the sum of squared residuals. Visualize how the slope $b = r rac{s_y}{s_x}$ and intercept relate to correlation, and interpret the line's predictive power for bivariate data.
Confidence Intervals
Construct confidence intervals using $ar{x} pm z^* rac{sigma}{sqrt{n}}$ to estimate population parameters. Visualize how confidence level, sample size, and variability affect interval width, and interpret what it means to be 95% confident about capturing the true parameter.
Binomial Distribution
Model discrete probability distributions for fixed trials with $P(X=k) = inom{n}{k}p^k(1-p)^{n-k}$. Visualize how the number of trials and success probability affect the shape, mean $mu = np$, and standard deviation $sigma = sqrt{np(1-p)}$ of binomial distributions.