Find the 95\% confidence interval for the data in Example 9-4.

Example 9-4.

A study was done to see if there is a difference between the non-mortgage debts of Generation X individuals and Millennials. Random samples of 10 individuals of each group were selected. The average debt of Generation X individuals was \(\$ 28,436\), and the average debt of Millennials was \(\$ 27,164\). The standard deviations of the samples were \(\$ 1647\) and \(\$ 1853\), respectfully. At \(\alpha=0.05\), can it be concluded that there is a difference in the means of the two samples? Assume the variables are normally distributed.