Question

1. A survey of 25 randomly sampled lawyers found that they averaged 65 billable hours a week, with a standard deviation of 6.25 hours.
   1. Develop a 99% confidence interval for the population mean for billable hours.
   2. Would it be reasonable to conclude that the population mean is 60 hours? How can you tell?
   3. How large of a sample is necessary to assess the population mean with an allowable error of 1 hour at 95% confidence?

Answer 1

a. 99% confidence level is

Mean -+ t*standard deviation /sqrt(n)

65-+ {2.797*6.25/sqrt(25)}

65-+ 3.49

( 61.51,68.49)

Here t is 99% t value at ( 25-1=24) degree of freedom.

b) No it is not reasonable to conclude that 60 is population mean, as we are 99% confident that population mean is within ( 61.51, 68.49) and 60 is beyond this interval.

C) sample size = (t*standard deviation /E)^2

Where E is margin of error.

n = (2.064*6.25/1)^2

= 166.4

Hence sample size should be 167.

Here t is 95% t value at 24 degree of freedom.