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. 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.

Sample Mean Sample Variance
Adults 77.5 4.5
Children 74.5 2.5
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 room temperature for adults exceeds that for children.
c) It can be concluded at the 99% confidence level that the true mean comfortable room temperature for children exceeds that for adults.
d) The probability that the true mean difference in comfortable room temperature is between -2.9 and 3.1 is equal to 0.99.

Answer 1

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.

Explanation: