A recent article in Healthy Life magazine claimed that the mean amount of leisure time per week for European men is $48.5$ hours. The distribution of leisure time amounts is reported to be approximately Normal. You believe the figure of 48.5 is too large and decide to conduct your own test. In a random sample of 25 European men, you find that the mean is $45$ hours of leisure per week and that the standard deviation of the sample is $7.8$ hours.
(a) Conduct the test and determine the $p$‒value. At $\alpha=0.01$ significance level, can you conclude that the information in the article is untrue?
$$\begin{cases} &H_{0}: &\mu>=48.5\\ &H_{1}: &\mu<48.5 \end{cases}$$
The $t$-statistic yields:
$$t\text{-stat} =\frac{45-48.5}{7.8/5}=-3.5/1.56\approx -2.244$$
$0.025<p\text{-value}<0.01$
so that
$p-\text{value}>\alpha$ implies that we do not reject $H_0$
(b) How would your answer to part (a) be affected if the distribution of leisure time amounts was uniform?
Especially, I wonder the question (b).