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statistics mathematics proofs involving congruence of integers proofs involving cartesian products of sets fundamental properties of set operations proofs involving sets proofs involving real numbers proofs involving divisibility of integers direct proofs proof by contrapositive proof by cases writing a proof proof evaluations trivial and vacuous proofs transitive inverse relation reflexive symmetric relations product sets confidence interval alternative hypothesis two-sided significance tests and null hypothesis one-sample t test the t distributions robustness of the t procedures matched pairs t procedures one-sample t confidence interval tests of significance test statistics p-values introduction to inference test for a population mean stating hypotheses statistical significance statistical confidence confidence interval for a population mean choosing the sample size estimating with confidence confidence intervals inference binomial mean and standard deviation sample proportions binomial formula sampling distributions for counts and proportions binomial distributions in statistical sampling normal approximation for counts and proportions binomial distributions for sample counts population distribution vs. sampling distribution central limit theorem sampling distribution of a sample mean the mean and standard deviation of the sample mean independence bayes’s rule conditional probability randomness probability general addition rules general multiplication rules general probability rules the law of large numbers rules for means and variances study of probability the mean of a random variable the variance of a random variable normal distributions as probability distributions random variable continuous random variables discrete random variables probability model probability distribution probability rules. the language of probability