A manufacturer claims that the average tar content of a certain kind of cigarette is \(\mu=14.0\). In an attempt to show that it differs from this value, five measurements are made of the tar content ( \(\mathrm{mg}\) per cigarette):

\[\begin{array}{lllll}14.5 & 14.2 & 14.4 & 14.3 & 14.6\end{array}\]

Show that the difference between the mean of this sample, \(\bar{x}=14.4\), and the average tar claimed by the manufacturer, \(\mu=14.0\), is significant at \(\alpha=0.05\). Assume normality.