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Hypothesis Tests
AP Statistics
| Term | Definition |
|---|---|
| interpreting a parameter (p or η) | true proportion/mean of (context) |
| null hypothesis | H0: p/η = #, assume it is true |
| alternative hypothesis | HA: -/η <,>, or ≠ # (< or > is one sided, ≠ is two sided) |
| interpreting a p-value | assuming p/η = H0 is true, there is a (p-value) probability of obtaining a (statistic, x-bar/p-hat) or more extreme by chance alone |
| p-value < level of significance | reject H0, we have evidence that HA is true |
| p-value > level of significance | fail to reject H0, we do not have evidence that HA is true |
| type 1 error | reject H0 when we should have failed to reject it (H0 is true but we say it is false), P(Type 1) = level of significance |
| type 2 error | fail to reject H0 when we should have rejected it (H0 is false and HA is true) P(Type 2)= 1-power |
| choose | 1-sample z/t test for p/η, define parameter, define H0 and HA, identify statistic (x-bar/p-hat) and level of significance |
| check | SRS with context, 10% (use p and not p-hat only for proportions), large counts/CLT |
| calculate | use formulas to find z-score/t-statistic and the p-value |
| conclude | p-value vs. significance level (< or >), decision about H0, concluding sentence always about HA (do we have convincing evidence that it is true?) |
| finding p-value for proportions | NormCdf, use z-score, symbol in HA, 0, 1 |
| finding p-value for means | tCdf, use t-score, symbol in HA, and df = n-1 |
| interpreting power | if HA is true (context) there is a (power) probability of finding convincing evidence to reject H0 (context) |
| power | probability of rejecting H0 given that HA is true |
| increasing power | increase sample size, increase level of significance, increase effect size (distance between true parameter and statistic), decreases P(Type 2 error) |
| power + P(Type 1) | 1.00 |
| decreasing the P(Type 2 error) | increases P(Type 1) and increases power) |
| H0 captured by confidence interval | fail to reject H0 |
| H0 not captured by confidence interval | reject H0 |
| conditions for a matched pairs t-test | SRS/random assignment, population is normal/CLT/graph has no skewness or outliers, DO NOT CHECK 10% UNLESS RANDOM ASSIGNMENT ISN'T STATED |
| matched pairs t-test | uses pairs that share a common characteristic, has one sample, mean of differences (calculate differences between both data sets and find the mean of difference distribution) |
| 2 sample t-test | 2 independent samples (ex. men and women), difference of means (calculate each mean of each data set separately then subtract them) |
| statistic/parameter for matched pairs test | x-bar sub. d and η sub. d |
| general formula for z/t-score | statistic-parameter/standard deviation |
| z-score formula | p-hat - p / √p(1-p)/n |
| t-score formula | x-bar - μ / standard deviation of sampling dist. / √n |
| name of hypothesis test for proportions | 1 sample z-test for p |
| name of hypothesis test for means/matched pairs | 1 sample t-test for η/η sub d |
| the p-value in a one sided test is | doubled for a 2-sided test, needs to be subtracted by 1 to account for < and > sides of a 2-sided test when going from 2 to 1 sided |
| the significance level in a one sided test | is cut in half (in terms of bell shaped curve diagram) for a 2-sided test |
| increasing P(Type 2 error) | decrease significance level, decrease P(Type 1), decrease sample size |
| picture for z distribution | bell shaped curve, N(0,1) |
| picture for t distribution | bell shaped curve, t(df) |
| calculating z-score/checking conditions for proportions | always use p and not p-hat |
Created by:
ts2819