Hypothesis Testing

Learn about hypothesis testing and confidence intervals.

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One method of statistical inferences is to test a hypothesis regarding a hypothetical population parameter value of β1\beta_1.

  • Null hypothesis H0H_0 :β1=0\beta_1 = 0. Trade openness has no effect on economic growth in the population.

  • Alternative hypothesis HaH_a : β10\beta_1 \neq 0. Trade openness has an effect on economic growth in the population.

t-test statistic

To test the null hypothesis directly, we have to construct a test statistic, denoted as t.

t=bβ1se(b)t = \frac{b-\beta_1}{se(b)}

This t-test statistic is similar in spirit to the t-test statistic on a hypothetical population mean introduced in thist_test . They’re both essentially the difference between the sample estimate and the hypothetical population parameter, weighted by the standard error of the sample estimate. In both scenarios, the test statistic follows a t-distribution and is referred to as the t-statistic. Take the results from model1 as an example.

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