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