A Sports Analyst Claims That the Mean Batting Average for Teams

A sports analyst claims that the mean batting average for teams in the American League is not equal to the
mean batting average for teams in the National League because a pitcher does not bat in the American League.
The data listed below are random, independent, and come from populations that are normally distributed.
Construct a 95% confidence interval for the difference in the means $\mu _ { 1 } - \mu _ { 2 } .$ Assume the population variances
are equal. $\text { American League }$
$\begin{array} { l l l l } 0.279 & 0.274 & 0.271 & 0.268 \\0.265 & 0.254 & 0.240 &\end{array}$ $\text { National League }$
$\begin{array} { l l l l } 0.284 & 0.267 & 0.266 & 0.263 \\0.261 & 0.259 & 0.256 &\end{array}$