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

Question

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

Quizplus · Accepted Answer

The psychologist wants to test if children prefer warmer temperatures than adults, implying children have a higher mean temperature preference. Thus, the alternative hypothesis should be that the mean temperature for children is greater than that for adults, which translates to $\mu_1 - \mu_2 < 0$.

In a Controlled Laboratory Environment, a Random Sample of 10