Hypothesis Testing and EViews p-values:
Suppose that we want to test a null hypothesis about a single parameter using its estimated value (for example a mean or a regression coefficient). We can do so using a t-test. To begin, suppose that the parameter to be estimated is β. We must first specify a null hypothesis and an alternative hypothesis.

2 tail test:
For a two tailed test, we want to test whether β is a particular value or not. We first set the value of β that we want to test. We’ll call this β0 to indicate that this will be the value of β under the null hypothesis. In a two tail test, the null and alternative hypotheses are: H0 : β = β 0 HA : β = β0 ˆ We proceed by estimating β. We denote the estimated value as β. This could for example be a sample mean estimate of the population mean, a least squared estimate of a regression coefficient, or a maximum likelihood estimate of a model coefficient, ˆ depending on the context. The estimate β is usually accompanied by a standard error ˆ to indicate how precisely it is estimated. We denote this standard error as se(β). This ˆ is a random variable with a sampling distribution. It will have reflects the fact the β different values in different samples. We can then form the following test statistic by computing the standardised statistic ˆ whereby we subtract the hypothesisized value β0 from the estimate β and divide by its standard error: t-stat = ˆ β − β0 ˆ se(β)

ˆ Again, this test statistic is a random variable since it depends on β, which is itself a random variable. To make inference and do hypothesis testing about the value of β, we must assume a distribution for the above test statistic. This distribution is based on the null hypothesis being true. Since, for an unbiased estimate, the test statistic has zero mean and is standardised by its standard error, the test statistic doesn’t depend on the 1

units of β,