Answer
a) Fail to reject the null hypothesis. b)$\mu_1-\mu_2$ is between -0.54 and 1.02.
Work Step by Step
a) Null hypothesis:$\mu_1=\mu_2$, alternative hypothesis:$\mu_1 \lt \mu_2$. 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 more than $\alpha=0.01$, because it is more than 0.1, hence we fail to reject the null hypothesis. b) The corresponding critical value using the table: $t_{\alpha/2}=t_{0.005}=2.764.$ The margin of error: $E=t_{\alpha/2}\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}=2.764\sqrt{\frac{0.89^2}{11}+\frac{0.66^2}{59}}=0.78.$ Hence the confidence interval $\mu_1-\mu_2$ is between $\overline{x_1}-\overline{x_2}-E$=(97.69-97.45)-0.78=-0.54 and$\overline{x_1}-\overline{x_2}+E$=(97.69-97.45)+0.78=1.02.
