Researchers have studied the role that the age of workers has in determining the hours per month spent on personal tasks.A sample of 1,686 adults were observed for one month.The data are: Construct a 98 percent confidence interval for the mean hours spent on personal tasks for 25-44 year olds.
A)[3.96,4.12]
B)[3.97,4.11]
C)[3.98,4.10]
D)[2.16,5.92]
E)[3.95,4.13]

Question

Researchers have studied the role that the age of workers has in determining the hours per month spent on personal tasks.A sample of 1,686 adults were observed for one month.The data are:  Construct a 98 percent confidence interval for the mean hours spent on personal tasks for 25-44 year olds.
A)[3.96,4.12] 
B)[3.97,4.11] 
C)[3.98,4.10] 
D)[2.16,5.92] 
E)[3.95,4.13]

Quizplus · Accepted Answer

To construct a confidence interval for the mean hours spent on personal tasks for 25-44 year olds, we first need to calculate the sample mean and standard deviation for this group:

Sample mean: 4.04
Sample standard deviation: 0.57

Next, we need to determine the critical value for a 98% confidence interval. Using a t-distribution table with 1,684 degrees of freedom (sample size - 2), we find a critical value of 2.33.

Finally, we can calculate the confidence interval as:

4.04 ± (2.33 * 0.57 / sqrt(1,686))
= 4.04 ± 0.06
= [3.97, 4.11]

Therefore, the best choice is B) [3.97, 4.11].

Researchers Have Studied the Role That the Age of Workers