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Topics of the top of my head: Population Sample Sample statistics Sample mean = 𝑥̅ = ….. and 𝑝̂ = …. Mode = Median = Sample variance = ….. Sample standard deviation = s = ….. Quartiles = Percentiles = Range = Inter-quartile range Statistic Parameter Random sample Random variable Probability Conditional Probabilities Multiplicative rule for independent events Multiplicative rule for joint event Additive rule for mutually exclusive events Distributions of Population Data Sampling for a statistic Graphing Pie chart Bar chart Histogram Dot plot Stem n leaf Series plot (line plot) Proportions (dichotomous events, two categories) Mean = p Variance = p(1-p) Std = √𝑝(1 − 𝑝) Binomial (counts out of n independent trials) 𝑛! 𝑦!(𝑛−𝑦)! 𝑝 𝑦 (1 − 𝑝)(𝑛−𝑦) Mean = np Variance = np(1-p) Std = √𝑛𝑝(1 − 𝑝) Normal distribution 𝑃(𝑦) = f(y) = 1 √2𝜋𝜎 2 1 (𝑦−𝜇)2 ) 𝜎2 exp(-2 mean = μ variance = 𝜎 2 std = σ Normal approximation of 𝑝̂ if np>15 and n(1-p)>15 Sampling distribution Mean=population mean, which is either μ general p binary/dichotomous np count Variance = population variance/sample size, which is either 𝜎 2 /n general p(1-p)/n binary/dichotomous np(1-p)/n count Central Limit Theorem: If n is large, sampling distribution of mean is approximately normal regardless of shape of population distribution. Confidence intervals 68/95/99.7 or 1/2/3 rule Standard score z = (x- 𝑥̅ )/n mean=0 std=1 uses (comparing distributions, for looking up in tables, testing hypotheses) Shapes of distributions Left skew Right skew Uni-modal Symmetric Bi-modal Type of decisions and Alpha Beta Power Type I error Type II error 5 Steps of a hypothesis test (1.) Assumptions (2) Hypotheses (3) Test statistic (4) P-value (5) Conclusion ( & interpretation in context of problem) Using all of the above to make inferences from sample about population. Basic R: Assignment: < Inputting sample data sets: c(x1,x2,….,xn) where c is for “combining” or “concatenation” Addition: x + p Subtractions: x - p Multiplication: x*p Division: x/n Square root: sqrt(y) Finding sum of values: sum(x) Mean: mean(x) Standard deviation: sd(x) Z-scores: scale(x) Finding probabilities from normal: P(Y<y) = pnorm(y,mean= , sd= ) Finding quanitles from normal : y = qnorm(p,mean=,sd=) Finding probabilities from binomial: P(Y<y) = pbinom(y,n,p) Finding quantiles from binomial: y = qbinom(p,y,n) Test of proportions (binomial counts): proportion.test(y,n,𝑝𝑜, , alternative=”two.sided”, conf.level=alpha, correct=FALSE) or alternative = “left” or “right”