Discussion
If the estimated \(\hat{\beta}_{2}\) is equal to the hypothesized β2, the 't' value will be equal to :
Answer: A
The t value will be 0.
The t statistic for testing the hypothesis that the true coefficient equals a given value is
\[ t = \frac{\hat{\beta}_{2} - \beta_{2}}{se(\hat{\beta}_{2})} \]
If the estimate equals the hypothesised value, the numerator is zero, so t = 0 whatever the standard error. The estimate then gives no evidence at all against the null hypothesis.
A value of 1 would need the estimate to differ from the hypothesis by exactly one standard error, and the standard error itself is the denominator, not the value of t. The option of 30 has no basis in the formula.
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