Two Means - Unknown, Unequal Variance: Videos & Practice Problems

Researchers are studying the effect of background music on concentration. One group of students studied with classical music, while another group studied in silence. Their concentration scores were recorded and summarized as follows:

Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Use degrees of freedom equal to the smaller of $n_1-1$ and $n_2-1$. Construct a $99\%$ confidence interval for the difference in mean concentration scores, where the difference is defined as the mean for the Classical Music group minus the mean for the Silence group.