Question 8.17: Test the null hypothesis that the coefficient of Pause is le......

The estimated coefficient of Pause is {\hat{\beta}_{2}} = 0.5652, with standard deviation s_{\hat{\beta}_{2}} = 0.2256. The null hypothesis is \beta_{2} ≤ 0.3. Under H_{0}, we take \beta_{2} = 0.3, so the quantity

t = \frac{\hat{\beta}_{2}\ −\ 0.3}{0.2256}

has a Student’s t distribution with 19 degrees of freedom. Note that the degrees of free-dom for the t statistic is equal to the degrees of freedom for error. The value of the t statistic is (0.5652 − 0.3) ∕ 0.2256 = 1.1755. The P-value is between 0.10 and 0.25. It is plausible that \beta_{2} ≤ 0.3.