Most People Are Definitely Dominant on One Side of Their

Most people are definitely dominant on one side of their body - either right or left. For some sports being able to use both
sides is an advantage, such as batting in baseball or softball. In order to determine if there is a difference in strength between
the dominant and nondominant sides, a few switch-hitting members of some school baseball and softball teams were asked
to hit from both sides of the plate during batting practice. The longest hit (in feet) from each side was recorded for each
player. The data are shown in the table below. $$\begin{array} { | c | c | c | } \hline \text { Batter } & \begin{array} { c } \text { Dominant } \\\text { Side }\end{array} & \text { Non-dominant } \\\hline \text { Side } \\\hline 1 & 142 & 119 \\\hline 2 & 144 & 118 \\\hline 3 & 153 & 126 \\\hline 4 & 148 & 119 \\\hline 5 & 146 & 121 \\\hline 6 & 149 & 125 \\\hline 7 & 138 & 116 \\\hline 8 & 145 & 120 \\\hline 9 & 153 & 124 \\\hline 10 & 160 & 138 \\\hline 11 & 163 & 135 \\\hline 12 & 170 & 144 \\\hline 13 & 169 & 142 \\\hline 14 & 151 & 128 \\\hline 15 & 152 & 131 \\\hline 16 & 167 & 141 \\\hline 17 & 164 & 140 \\\hline 18 & 165 & 140 \\\hline 19 & 163 & 138 \\\hline\end{array}$$
-Does this sample indicate that there is a difference in the distance a ball is hit by batters
who are switch-hitters? Test an appropriate hypothesis and state your conclusion.