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

A sports scientist is investigating whether there is a difference in the average sprint times (in seconds) between athletes who use a new training program and those who use a standard program. The following data were collected:

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 $95$% confidence interval for the difference in mean sprint time, where the difference is defined as the mean for the New Program minus the mean for the Standard Program.