A random sample of 40 observations of a random variable \(X\) and a random sample of 50 observations of a random variable \(Y\) are taken. The resulting values for the sample means, \(\bar{x}\) and \(\bar{y}\), and the unbiased estimates, \(s_{x}^{2}\) and \(s_{y}^{2}\), for the population variances are as follows.
\(\bar{x}=24.4 \quad \bar{y}=17.2 \quad s_{x}^{2}=10.2 \quad s_{y}^{2}=11.1\)

Find a \(90 \%\) confidence interval for the difference between the population means of \(X\) and \(Y\).