14 A random sample of 40 adults with no children under the a

14) A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.19 hours, with a standard deviation of 2.38 hours. A random sample of 40 adults with children under the age of 18 results in a mean deaily leisure time of 4.38 hours, with a standard deviation of 1.78 hours. Construct and interpret a 95% confidence interval for the mean difference in leisure time between adults with no children and adults with children (u1 - u2).

Let u1 represent the mean leisure hours of adults with no children under the age of 18 and u2 represent the mean leisure hours of adults with children under the age of 18.

(a) The 95% confidence interval for (u1 - u2) is the range from _ hours to _ hours. (round to two decimal places as needed.)

(b) What is the interpretation of this confidence interval?

A) There is 95% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours.

B) There is a 95% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours.

C) There is a 95% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours.

D) There is 95% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours

Solution

B) There is a 95% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours.