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

H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 3

vs.

H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) \neq 0

H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 0

vs.

H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 0

H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 0

vs.

H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) < 0

Identify the Rejection Region That Should Be Used to Test H0:σ12=σ22H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } { } ^ { 2 }H0​:σ12​=σ2​2

Multiple Choice

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Identify the Rejection Region That Should Be Used to Test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } { } ^ { 2 }$

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