A Womenʹs Advocacy Group Claims That Women Golfers Receive Significantly $\mu _ { 1 } - \mu _ { 2 }$

A womenʹs advocacy group claims that women golfers receive significantly less prize money than their male
counterparts when they win first place in a professional tournament. The data listed below are the first place
prize monies from male and female tournament winners. Assume the samples are random, independent, and
come from populations that are normally distributed. Construct a 99% confidence interval for the difference in
the means $\mu _ { 1 } - \mu _ { 2 }$ Assume the population variances are not equal. $\text { Female Golfers }$
$\begin{array} { l l l l l } 180,000 & 150,000 & 240,000 & 195,000 & 202,500 \\120,000 & 165,000 & 225,000 & 150,000 & 315,000\end{array}$ $\text { Male Golfers }$
$\begin{array} { l l l l l } 864,000 & 810,000 & 1,170,000 & 810,000 & 630,000 \\1,050,000 & 945,000 & 1,008,000 & 900,000 & 756,000 \\630,000 & 900,000 & & &\end{array}$