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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 (r2) 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) pr (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)**

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**

Ho: µd = hypothesized value Ha: µd < > ≠ 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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