## Elementary Statistics (12th Edition)

$H_{0}:\mu_d=6.8,$ $H_{a}:\mu_d\ne6.8$. The test statistic is:$t=\frac{\overline{d}-\mu_d}{s_d/\sqrt{n}}=\frac{1.1791-6.8}{3.8883/\sqrt{67}}=-11.833.$ The P is the corresponding probability using the table with df=67-1=66, hence P is less than 0.01. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P is less than$\alpha=0.05$, hence we reject the null hypothesis. Hence the differences don't seem to be 6.8.