Introductory Statistics: study guide and practice
Also known as: stat 101, stat 1342, mat 120, math 1342, sta 2023, stat 200, elementary statistics, statistics for social sciences, introduction to statistics, business statistics
What you will be able to do
- Summarise data with measures of centre and spread
- Calculate and interpret probabilities, including conditional probability
- Use the binomial distribution and expected value
- Use the normal distribution and z-scores
- Explain sampling distributions and the Central Limit Theorem
- Build and interpret confidence intervals
- Carry out and interpret hypothesis tests
- Fit and interpret a simple linear regression
Topics
- Descriptive statisticsSummarise a data set with its centre (mean, median, mode) and spread (range, IQR, standard deviation).
- ProbabilityThe rules for computing the chance of events: complements, addition, multiplication and conditional probability.
- Discrete random variables and the binomial distributionExpected value of a random variable and the binomial model for counting successes in repeated trials.
- The normal distribution and z-scoresThe bell curve, the empirical rule and standardising values with z-scores.
- Sampling and the Central Limit TheoremWhy sample statistics vary, how to sample without bias, and how the Central Limit Theorem lets us use the normal curve.
- Confidence intervalsEstimate a population mean or proportion with a range of plausible values, and interpret the confidence level correctly.
- Hypothesis testingDecide whether sample data are strong evidence against a claim, using test statistics, p-values and significance levels.
- Correlation and linear regressionMeasure the strength of a linear relationship with r and predict one variable from another with the least-squares line.