#### Answer

There is not sufficient evidence to support that the mean wake time is less than 102.8 minutes.

#### Work Step by Step

$H_{0}:\mu=102.8$. $H_{a}:\mu < 102.8.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{98.9-102.8}{42.3/\sqrt{16}}=-0.369$ The P-value is the interval of probabilities between which the value of the test-statistic lies in the table with degree of freedom=sample size-1=40-1=39, hence P is more than 0.1. 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 $\alpha=0.1$, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to support that the mean wake time is less than 102.8 minutes.