Senior management of a consulting services firm is concerned about a growing decline in the firm's weekly number of billable hours. The firm expects each professional employee to spend at least 40 hours per week on work. In an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. Rather than reviewing the records of all the firm's full-time employees, the management randomly selected a sample of size 50 from the available frame. The sample mean and sample standard deviations were 48.5 and 7.5 hours, respectively.
(A) Construct a 99% confidence interval for the standard deviation of the number of hours this firm's employees spend on work-related activities in a typical week.(B) Interpret the 99% confidence interval constructed in (A).(C) Given the target range of 40 to 60 hours of work per week, should senior management be concerned about the number of hours their employees are currently devoting to work? Explain why or why not.
What will be an ideal response?
(A) 
. The confidence interval formulas for 
(not presented in the book) are:
Lower limit = 
=5.936
Upper limit = 
(B) We are 99% confident that the population standard deviation 
is between 5.936 and 10.057.
(C) The best guess for the population mean is 48.5 hours per week, and about 95% of all employees are within 2 standard deviations of this, where we are almost sure (99% sure) that this standard deviation is between 5.9 and 10.1. But even if the standard deviation is only 5.9, then 48.5
standard deviations will produce the range 36.7 to 60.3. Maybe management should be concerned.
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