Research has been conducted that studies 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% confidence interval for the mean hours spent on personal tasks for 25-44 year olds.

Question

Research has been conducted that studies 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% confidence interval for the mean hours spent on personal tasks for 25-44 year olds.

Quizplus · Accepted Answer

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

sample mean = 4.04 hours/month
sample standard deviation = 0.271 hours/month

Next, we calculate the margin of error using the t-distribution with n-1 degrees of freedom (where n=sample size):

t(0.99, 1684) = 2.338

margin of error = t * (standard deviation / square root of sample size)
                 = 2.338 * (0.271 / sqrt(1686))
                 = 0.067

Finally, we construct the 98% confidence interval:
confidence interval = sample mean +/- margin of error
                    = 4.04 +/- 0.067
                    = [3.97, 4.11]

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

Research Has Been Conducted That Studies the Role That the Age