Determine the null and alternative hypotheses 2 Specify the test statistic and

# Determine the null and alternative hypotheses 2

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1. Determine the null and alternative hypotheses.2. Specify the test statistic and its distribution if the null hypothesis is true.3. Select αand determine the rejection region.4. Calculate the sample value of the test statistic.5. State your conclusion. 3.4 Examples of Hypothesis Tests STEP-BY-STEP PROCEDURE FOR TESTING HYPOTHESES Principles of Econometrics, 4t h Edition Page 44 Chapter 3: Interval Estimation and Hypothesis Testing 3.4.1a One-tail Test of Significance The null hypothesis is H 0 : β 2 = 0 The alternative hypothesis is H 1 : β 2 > 0 The test statistic is Eq. 3.7 In this case c = 0, so t = b 2 /se( b 2 ) ~ t ( N 2) if the null hypothesis is true Select α = 0.05 The critical value for the right-tail rejection region is the 95 th percentile of the t- distribution with N 2 = 38 degrees of freedom, t (0.95,38) = 1.686. Thus we will reject the null hypothesis if the calculated value of t ≥ 1.686. If t < 1.686, we will not reject the null hypothesis. 3.4 Examples of Hypothesis Tests Principles of Econometrics, 4t h Edition Page 45 Chapter 3: Interval Estimation and Hypothesis Testing 3.4.1a One-tail Test of Significance Using the food expenditure data, we found that b 2 = 10.21 with standard error se( b 2 ) = 2.09 The value of the test statistic is: Since t = 4.88 > 1.686, we reject the null hypothesis that β 2 = 0 and accept the alternative that β 2 > 0 That is, we reject the hypothesis that there is no relationship between income and food expenditure, and conclude that there is a statistically significant positive relationship between household income and food expenditure 2 2 10.21 4.88 se 2.09 b t b 3.4 Examples of Hypothesis Tests 