In a Controlled Laboratory Environment, a Random Sample of 10

In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds
Most comfortable. The data are summarized below: $\begin{array}{lcc}\hline & \text { Sample Mean } & \text { Sample Variance } \\\hline \text { Adults (1) } & 77.5^{\circ} \mathrm{F} & 4.5 \\\text { Children (2) } & 74.5^{\circ} \mathrm{F} & 2.5 \\\hline\end{array}$

If the psychologist wished to test the hypothesis that children prefer warmer room temperatures than adults, which set of hypotheses would he use?

A) $H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 0$ vs. $H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 0$
B) $H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 0$ vs. $H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) < 0$
C) $H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 3$ vs. $H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) \neq 0$
D) $H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 0$ vs. $H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) > 0$