Researchers 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 93 percent confidence interval for the mean hours spent on personal tasks for 45-64 year olds.
A)[4.26,4.36]
B)[4.25,4.37]
C)[4.27,4.35]
D)[4.28,4.34]
E)[2.83,5.79]

Question

Researchers 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 93 percent confidence interval for the mean hours spent on personal tasks for 45-64 year olds.
A)[4.26,4.36] 
B)[4.25,4.37] 
C)[4.27,4.35] 
D)[4.28,4.34] 
E)[2.83,5.79]

Quizplus · Accepted Answer

To construct a confidence interval, we need the sample mean, standard deviation, sample size, and the level of confidence.

Sample mean (x̄) for 45-64 year olds = 4.31
Sample standard deviation (s) for 45-64 year olds = 1.29
Sample size (n) for 45-64 year olds = 648
Level of confidence = 93%

The formula for the confidence interval for a population mean is:

x̄ ± t*(s/√n)

where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-score obtained from the t-distribution table for a given level of confidence and degrees of freedom (df = n-1).

Using a t-distribution table for df = 647 and a level of confidence of 93%, we find the t-score to be 1.812.

Plugging in the values, we get:

4.31 ± 1.812*(1.29/√648)

= 4.31 ± 0.054

= [4.25, 4.37]

Therefore, the 93% confidence interval for the mean hours spent on personal tasks for 45-64 year olds is [4.25, 4.37].

The correct answer is B.

Researchers Studied the Role That the Age of Workers Has