Hypothesis Testing

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

• Null hypothesis $H_0$ :$\beta_1 = 0$. Trade openness has no effect on economic growth in the population.

• Alternative hypothesis $H_a$ : $\beta_1 \neq 0$. 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.

$$t = \frac{b-\beta_1}{se(b)}$$

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.