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AP Statistics Course Review

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Exploring Data Variables can be categorical or quantitative Discrete or continuous For categorical data, we use bar charts Numerical data can be displayed using a dotplot, stemplot, box-and-whisker plot, histogram or cumulative frequency plot Remember histograms have no spaces (unless a category has none) Must include key with stemplot Always label axes and make sure you read the axes when interpreting a graph.

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Commenting on a graph Shape: symmetric, skewed, unimodal, uniform Center: Mean and median Spread: Range, standard deviation, Iqr, gaps, outliers (1.5x iqr) added to quartile

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Effect of changing units Changing units will change measures of center and spread by the same ratio as the multiplier. Adding or subtracting the same constant will change measures of center in a similar manner but will not change measures of spread. Trial Run 1

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Scatterplots Bivariate, explanatory, response Correlation coefficient (r) -1 to 1 R does not change when you switch x and y, nor will it change when you multiply or add Only measures strength of linear relationship Affected by outliers Lurking variables Danger of extrapolation

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Coefficient of determination (r 2 ) Residuals (observed – predicted) Influential points Transformations Trial run

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Sampling Census, survey, experiment, observational study Parameter (population) statistic (sample) Convenience, SRS, stratified, cluster, systematic Bias: undercoverage, nonresponse, response Placebo, blind, randomization, replication, confounding variable

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Experimental designs: completely randomized, blocks, matched pairs Trial run

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Probability Law of large numbers: long-term relative frequency gets closer to true freq. as # trials increases Disjoint (mutually exclusive): cannot occur simultaneously Mand and ort Conditional probability: Independence: knowing one has occurred doesn’t change chance of the other

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Probability distributions Matches all possible values of variable with probability of it happening All probabilities must be between 0 and 1 Total of probabilities must be 1 Mean: Variance

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Binomial Random Variables Fixed number of trials, success or failure P remains constant each trial Each trial is independent (nCr) p r (1-p) n-r Mean: np Variance: np(1-p)

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Geometric Random Variable Success or failure P constant, each trial independent How many times until …. Probability k trials occur before … p (1-p) k-1 Trial run

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Combining Variables Mean (x+y) = mean (x) + mean (y) Mean (x-y) = mean (x) – mean (y) If independent: variance (x+y)= var(x)+var(y)

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Normal distributions Z-score Standardize endpoints, find area under curve Trial run

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Sampling distributions All possible random samples are taken and used to create a sampling distribution of the sample mean Standard dev. : Central Limit Theorem: as the size of an SRS increases, the shape of the sampling dist. tends toward normal

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Hypothesis Testing Sample Proportion Ho: Ha: Test Statistic Pvalue Assumptions: p is from a random sample Sample size is large (np>10 and n(1-p)>10) Sample no more than 10% of population

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Sample Mean Ho: Ha: Test Statistic P value Assumptions: from a random sample Sample size is large (>30) or population distribution is approximately normal

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Hypothesis Testing Difference in 2 sample proportions: Ho: Ha: Test statistic: P value Assumptions: independently chosen random samples or treatments were assigned at random to individuals Both sample sizes are large (np>10, n(1-p)>10 works for both of them

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Hypothesis Testing Difference in two sample means Ho: Ha: Test Statistic P value Assumptions: 2 sample are independently selected random samples Sample size large (>30) or population distributions are approximately normal

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Hypothesis Testing Paired t test comparing 2 population means H o : µ d = hypothesized value H a : µ d ≠ hypothesized value Test statistic: Pvalue: Assumptions: Samples are paired Random samples from a pop. Of differences Sample size is large (>30) or population distribution of differences is about normal

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Hypothesis Testing Chi-Square GOF Ho: Ha: Test Statistic P value Assumptions: based on random sample Sample size is large – every expected cell count at least 5 Degrees of freedom?

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Hypothesis Testing Chi-Square Test of Homogeneity or Independence (2 way table) Ho: There is no relationship between __and _ Ha: Ho not true Test Statistic: P value Assumptions: independently chosen random samples or random assignation to groups All expected cell counts are at least 5 Degrees of freedom?

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Hypothesis Testing (last one!!) Chi-square test for slope Ho: Ha: Test statistic: P value Assumptions: dist. of e has mean value=0, std. dev. of e does not depend on x, dist. of e is normal, random dev. of e are independent of each other Degrees of freedom: n-2

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Confidence Intervals Statistic ± margin of error(also called bound) Margin of error is combination of 2 numbers: (Critical value ) (standard error)

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