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)1.6279
B)0.7000
C)0.1871
D)0.8367

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)1.6279
B)0.7000
C)0.1871
D)0.8367

Quizplus · Accepted Answer

The standard error of the estimate for the difference in mean comfortable room temperatures between two independent groups can be calculated using the formula: $\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$, where $s_1^2$ and $s_2^2$ are the sample variances, and $n_1$ and $n_2$ are the sample sizes for the two groups, respectively. Plugging in the given values: $\sqrt{\frac{4.5}{10} + \frac{2.5}{10}} = \sqrt{0.45 + 0.25} = \sqrt{0.7} = 0.8367$.

In a Controlled Laboratory Environment, a Random Sample of 10