Variance of Differences of Random Variables.
Introduction to descriptive statistics and central tendency. Ways to measure the average of a set: median, mean, mode.
The difference between the mean of a sample and the mean of a population.
Using the variance of a sample to estimate the variance of a population.
Review of what we've learned. Introduction to the standard deviation.
Introduction to random variables and probability distribution functions.
Probability density functions for continuous random variables.
(Long-26 minutes) Presentation on spreadsheet to show that the normal distribution approximates the binomial distribution for a large number of trials.
Discussion of how "normal" a distribution might be.
Using the empirical rule (or 68-95-99.7 rule) to estimate probabilities for normal distributions.
Using the Empirical Rule with a standard normal distribution.
Introduction to the central limit theorem and the sampling distribution of the mean.
The central limit theorem and the sampling distribution of the sample mean.
More on the Central Limit Theorem and the Sampling Distribution of the Sample Mean.
Standard Error of the Mean (a.k.a. the standard deviation of the sampling distribution of the sample mean.
Figuring out the probability of running out of water on a camping trip.
Mean and Variance of Bernoulli Distribution Example.
Bernoulli Distribution Mean and Variance Formulas.
Finding the 95% confidence interval for the proportion of a population voting for a candidate.
Finding the 95% confidence interval for the proportion of a population voting for a candidate.
Constructing small sample size confidence intervals using t-distributions.
T-Statistic Confidence Interval (for small sample sizes).
Large Sample Proportion Hypothesis Testing.
Variance of Differences of Random Variables.
Confidence Interval of Difference of Means.
Clarification of Confidence Interval of Difference of Means.
Hypothesis Test Comparing Population Proportions.
Introduction to the idea that one can find a line that minimizes the squared distances to the points.
Proof (Part 1) Minimizing Squared Error to Regression Line.
Proof (Part 3) Minimizing Squared Error to Regression Line.
Proof (Part 4) Minimizing Squared Error to Regression Line.
Proof Part 2 Minimizing Squared Error to Line.
R-Squared or Coefficient of Determination.
Calculating R-Squared to see how well a regression line fits data.
Covariance, Variance and the Slope of the Regression Line.
Pearson's Chi Square Test (Goodness of Fit).
Analysis of Variance 1 - Calculating SST (Total Sum of Squares).
Analysis of Variance 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).
Analysis of Variance 3 -Hypothesis Test with F-Statistic.