Lecture07extranotes

# Lecture07extranotes - P = 0.2758 P = 0.0735 Introduction to...

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Introduction to Inference Tests of Significance Section 6.2 (Continued) © 2009 W.H. Freeman and Company P = 0.1711 P = 0.2758 P = 0.0892 P = 0.0735 P = 0.01 P = 0.05 When the shaded area becomes very small, the probability of drawing such a sample at random gets very slim. Often , a P-value of 0.05 or less is considered significant : The phenomenon observed is unlikely to be entirely due to chance event from the random sampling. Significant P-value ??? The significance level ! We compare the P-value with a level that we regard as decisive called the significance level , ! . This value is decided arbitrarily before conducting the test. ! If the P-value is equal to or less than ! ( P ! ! ), then we reject H 0 . ! If the P-value is greater than ! ( P > ! ), then we fail to reject H 0 . Does the packaging machine need revision? Two-sided test. The P - value is 4.56%. * If ! had been set to 5%, then the P-value would be significant. * If ! had been set to 1%, then the P-value would not be significant. When the z score falls within the rejection region (shaded area on the tail-side), the p-value is smaller than ! and you have shown statistical significance. z = -1.645 Z One-sided test, ! = 5% Two-sided test, ! = 1%

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Rejection region for a two-tail test of ! with ! = 0.05 (5%) A two-sided test means that ! is split between both tails of the curve, thus: -A middle area C of 1 " ! = 95% -An upper tail area of ! /2 = 0.025 -A lower tail area of ! /2 = 0.025 0.025 0.95 0.025 Test of significance 1. State the null hypothesis H 0 and the alternative hypotheses H a . The test is designed to assess the strength of evidence against H 0 ; H a is the statement we will accept if we reject H 0 .
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