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) 0.8367
B) 0.7000
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) 0.8367
B) 0.7000
C) 1.6279
D) 0.1871

Quizplus · Accepted Answer

The standard error for the difference in means is calculated using the formula: $\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$. Substituting the given variances and sample sizes, we get $\sqrt{\frac{4.5}{10} + \frac{2.5}{10}} = \sqrt{0.45 + 0.25} = \sqrt{0.7} \approx 0.8367$.

In a Controlled Laboratory Environment, a Random Sample of 10