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Lecture07 - The significance level Introduction to...

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Introduction to Inference Tests of Significance Section 6.2 (Continued) © 2009 W.H. Freeman and Company 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% 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
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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 . 2. Select a significance level. 3. Calculate the test statistic . 4. Find the P-value for the observed data. 5. State a conclusion. If P -value ! " reject H o If P -value > " do not reject H o Confidence intervals to test hypotheses Because a two-sided test is symmetrical, you can also use a confidence interval to test a two-sided hypothesis.
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