Ryan Warshavsky Percentile The nth percentile is a point such n of points in the data are left of this point Independence if one does not influence the other knowing A doesn t give info about B Varience s2 x1 x 2 xn x 2 n 1 Shows variation about the mean SD x s tandard Deviation varience np 1 p z value mean standard deviation x np np 1 p mean E x x p x var x E x 2 E x2 E x c E x c Var x c var x SD x c SD x E ax aE x Var ax a2var x SD ax a SD x E x y E x E y Var x y Var x var y Binomial Distribution has N number of independent trials each has two outcomes success or failure P success is constant P x n x n x p x p 1 n x P x probability of x successes in n trials x of successes p probability of success n sample size E x np np 1 p Sampling Distributions and Confidence Intervals for Proportions count of successes x n n p p p Confidence Intervals SD p p 1 p Margin of Error ME p Z p 1 p n z m 2 p 1 p ALWAYS ROUND UP n Confidence Level 90 95 98 99 99 9 Z 1 645 1 96 2 326 2 576 3 29 Testing Hypotheses about proportions Step 1 H 0 P P0 P known H a P P0 or H a P P0 or H a P P0 Step 2 Test Statistic Step 3 P Value z value mean standard deviation P P0 P0 1 P0 n Area under curve probability of seeing something as extreme or more extreme than the data we already observed under the assumption of the null hypothesis Small P Value reject H 0 small P value is evidence against H 0 Often 05 or less less than Step 4 compare to alpha 1 sided has alpha in the tail 2 sided has alpha 2 in each tail Type I error null hypothesis is true but we reject it Type II error null hypothesis is false but we refuse to reject it 10 05 01 001 1 sided 1 28 1 645 2 33 3 09 2 sided 1 645 1 96 2 576 3 29
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