Two manufacturing plants produce the same component. A random sample from plant X yields $n_1=25$, ${\bar{x}}_1=45.2$, $s_1=5.4$. A random sample from plant Y yields $n_2=30$, ${\bar{x}}_2=42.6$, $s_2=6.1$. Assume the populations are approximately normal with equal variances. Construct a $95\%$ confidence interval for ${\mu }_1-{\mu }_2$.