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:

$$\begin{array} { l c c }
\hline & \text { Sample Mean } & \text { Sample Variance } \
\hline \text { Adults (1) } & 77.5 ^ { \circ } \mathrm { F } & 4.5 \
\text { Children (2) } & 74.5 ^ { \circ } \mathrm { F } & 2.5 \
\hline
\end{array}$$ Find the standard error of the estimate for the difference in mean comfortable room temperatures between adults and children.
A) 0.7000
B) 0.8367
C) 1.6279
D) 0.1871

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:

$$\begin{array} { l c c } 
\hline & \text { Sample Mean } & \text { Sample Variance } \
\hline \text { Adults (1) } & 77.5 ^ { \circ } \mathrm { F } & 4.5 \
\text { Children (2) } & 74.5 ^ { \circ } \mathrm { F } & 2.5 \
\hline
\end{array}$$ Find the standard error of the estimate for the difference in mean comfortable room temperatures between adults and children.
A) 0.7000
B) 0.8367
C) 1.6279
D) 0.1871

Quizplus · Accepted Answer

The standard error for the difference in means is calculated using the formula: SE = sqrt((s1^2/n1) + (s2^2/n2)), where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes. Plugging in the values: SE = sqrt((4.5/10) + (2.5/10)) = sqrt(0.45 + 0.25) = sqrt(0.7) ≈ 0.8367.

In a Controlled Laboratory Environment, a Random Sample of 10