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【正文】 t a t i s t i c o u r u s e t h e n w i l lWe?? : ?f o r s t a t i s t i c t h e f o r m t on e e df i r s t eo u r t e s t w p e r f o r m Totsettjjjbbbb?9 t Test: OneSided Alternatives Besides our null, H0, we need an alternative hypothesis, H1, and a significance level H1 may be onesided, or twosided H1: bj 0 and H1: bj 0 are onesided H1: bj ? 0 is a twosided alternative If we want to have only a 5% probability of rejecting H0 if it is really true, then we say our significance level is 5% 10 OneSided Alternatives (cont) Having picked a significance level, a, we look up the (1 – a)th percentile in a t distribution with n – k – 1 df and call this c, the critical value We can reject the null hypothesis if the t statistic is greater than the critical value If the t statistic is less than the critical value then we fail to reject the null 11 yi = b0 + b1xi1 + … + bkxik + ui H0: bj = 0 H1: bj 0 c 0 a ?1 ? a? OneSided Alternatives (cont) Fail to reject reject 12 Onesided vs Twosided Because the t distribution is symmetric, testing H1: bj 0 is straightforward. The critical value is just the negative of before We can reject the null if the t statistic –c, and if the t statistic than –c then we fail to reject the null For a twosided test, we set the critical value based on a/2 and reject H1: bj ? 0 if the absolute value of the t statistic c 13 yi = b0 + b1Xi1 + … + bkXik + ui H0: bj = 0 H1: bj 0 c 0 a/2 ?1 ? a? c a/2 TwoSided Alternatives reject reject fail to reject 14 Summary for H0: bj = 0 Unless otherwise stated, the alternative is assumed to be twosided If we reject the null, we typically say “xj is statistically significant at the a % level” If we fail to reject the null, we typically say “xj is statistically insignificant at the a % level” 15 Testing other hypotheses A more general form of the t statistic recognizes that we may want to test something like H0: bj = aj In this case, the app
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