Your Textbook Reports the Following Result from an Two-Way Fixed $\widehat{\text { FatalityRate }}$

Your textbook reports the following result from an two-way fixed effects (entity and time fixed effects)regression model: $\widehat{\text { FatalityRate }}$ = -0.66 BeerTax + StateFixedEffects + TimeFixedEffects
(0.36)
Where the number in parenthesis is the heteroskedasticity- and autocorrelation-consistent (HAC)standard error.
a. Calculate the t-statistic. Can you reject the null hypothesis that the slope coefficient is zero in the population, using a two-sided test and a 5% significance level?
b. Given that economic theory suggests that the population slope is negative under the alternative hypothesis, is it possible to use a one-sided test here? In that case, does your conclusion change?
c. Using only heteroskedasticity-robust standard errors, but not HAC standard errors, the value in parenthesis becomes 0.25. Repeat the calculations in (a)and report your decision based on a two-sided test.
d. Since the coefficient becomes more statistically significant in (d), should this influence your choice of standard errors? Why or why not?