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 follow. Construct a 98 percent confidence interval for the mean hours spent on personal tasks for 25- to 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 follow.  Construct a 98 percent confidence interval for the mean hours spent on personal tasks for 25- to 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 the confidence interval, we can use the following formula:

CI = x̄ ± z* (s/√n)

where x̄ is the sample mean, z* is the z-score corresponding to the desired confidence level (98% in this case), s is the sample standard deviation, and n is the sample size.

First, we need to calculate the sample mean and standard deviation for the 25-44 age group:

x̄ = 4.04 hours 
s = 1.04 hours

Next, we need to find the z-score that corresponds to a 98% confidence level. Using a standard normal distribution table or calculator, we find that the z-score is 2.33.

Finally, we plug in the values to get the confidence interval:

CI = 4.04 ± 2.33 * (1.04/√1686)

CI = 4.04 ± 0.056

CI = [3.97, 4.11]

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

Researchers Have Studied the Role That the Age of Workers