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: $$\begin{array} { l c c }
\hline & \text { Sample Mean } & \text { Sample Variance } \
\hline \text { Adults (1) } & 77.5 ^ { \circ } \mathrm { F } & 4.5 \
\text { Children (2) } & 74.5 ^ { \circ } \mathrm { F } & 2.5 \
\hline
\end{array}$$ Suppose that the psychologist decides to construct a 99% confidence interval for the difference in mean comfortable room temperatures instead of proceeding with a test of hypothesis. The 99% confidence interval turns out to be (-2.9, 3.1). Select the correct statement.
A) It cannot be concluded at the 99% confidence level that there is actually a difference between the true mean comfortable room temperatures for the two groups.
B) It can be concluded at the 99% confidence level that the true mean comfortable room temperature for children exceeds that for adults.
C) It can be concluded at the 99% confidence level that the true mean room temperature for adults exceeds that for children.
D) It can be concluded at the 99% confidence level that the true mean comfortable room temperature is between -2.9 and 3.1.

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: $$\begin{array} { l c c } 
\hline & \text { Sample Mean } & \text { Sample Variance } \
\hline \text { Adults (1) } & 77.5 ^ { \circ } \mathrm { F } & 4.5 \
\text { Children (2) } & 74.5 ^ { \circ } \mathrm { F } & 2.5 \
\hline
\end{array}$$ Suppose that the psychologist decides to construct a 99% confidence interval for the difference in mean comfortable room temperatures instead of proceeding with a test of hypothesis. The 99% confidence interval turns out to be (-2.9, 3.1). Select the correct statement.
A) It cannot be concluded at the 99% confidence level that there is actually a difference between the true mean comfortable room temperatures for the two groups.
B) It can be concluded at the 99% confidence level that the true mean comfortable room temperature for children exceeds that for adults.
C) It can be concluded at the 99% confidence level that the true mean room temperature for adults exceeds that for children.
D) It can be concluded at the 99% confidence level that the true mean comfortable room temperature is between -2.9 and 3.1.

Quizplus · Accepted Answer

The confidence interval includes 0, so we cannot conclude that there is a difference between the true mean comfortable room temperatures for the two groups.

In a Controlled Laboratory Environment, a Random Sample of 10