critical critical t for one sided test and t for two sided test critical

Critical critical t for one sided test and t for two

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critical critical t for one-sided test, and t for two-sided test. critical critical n K , n K , / 2 t t K is the number of the parameters in the model. Then compare the test statistic with the test critical values. At last, reject H 0 if the absolute value of t-statistic is larger than the critical value, i.e., t-statistic> c ritical . Example: A consultant believes that on other similar neighbourhood households will spend an additional $7.50 on food per $100 additional income. 1. Set up the hypothesis 0 2 1 2 H : 7.5 against H : 7.5 (2.28) 2. Find the test statistic 2 2 2 2 7.5 10.21 7.5 1.29 ( ) 2.09 2.09 b b t se b (2.29) 3 Find the critical value at 5 and ( 0.025,40 2 ) ( 0.975,40 2 ) . 0.0 . t 2.024 t 2.024  
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27 4. Since -2.204 <1.29 < 2.204 we do not reject the null hypothesis that =7.5. The sample data are consistent with the conjecture households will spend an additional $7.50 on food per additional $100 income increase. The following summarizes the rejection regions for one sided test. a) When testing the null hypothesis H 0 : β k = c against the alternative hypothesis H 1 : β k < c , reject the null hypothesis and accept the alternative hypothesis if t t (1- α ; N -2). Figure 8 Rejection region for a one-tail test of H 0 : β k = c against H 1 : β k < c b) When testing the null hypothesis H 0 : β k = c against the alternative hypothesis H 1 : β k > c , reject the null hypothesis and accept the alternative hypothesis if t t (1- α ; N -2) . Figure 9 Rejection region for a one-tail test of H 0 : β k = c against H 1 : β k > c c) When testing the null hypothesis H 0 : β k = c against the alternative hypothesis H 1 : β k c , reject the null hypothesis and accept the alternative hypothesis if t t (1- α ; N -2) or t t (1- α ; N -2) .
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28 Figure 10 Rejection region for a test of H 0 : β k = c against H 1 : β k c 12.2 The p-value It has become standard practice to report the probability value of the test (p-value for an abbreviation) when reporting the outcome of statistical hypothesis tests. If we have the p- value of a test, p , we can determine the outcome of the test by comparing the p-value to the chosen level of significance, α, without looking up or calculating the critical values. p-Value rule states that Reject the null hypothesis when the p- value is less than, or equal to, the level of significance α. That is, if p ≤ α then reject H 0 . If p > α then do not reject H 0 . If t is the calculated value of the t-statistic, then: if H1: β K > c p = probability to the right of t if H1: β K < c p = probability to the left of t if H1: β K ≠ c p = sum of probabilities to the right of |t| and to the left of |t| Figure 11 The p-value for a two-tail test of significance 2 2 7.5 10.21 7.5 1.29 se 2.09 b t b 20 . 0 29 . 1 29 . 1 38 38 t P t P p
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29 If we choose α =0.05, α =0.10 or even α =0.20, we will fail to reject the null hypothesis, because p> α.
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