A utility company's line clearance crew must estimate personnel requirements for the strategic plan of the company. Consequently, they need to estimate the mean number of labor-hours required to perform each of the following three clearance tasks: trim a tree, remove a tree, or cut a square foot of brush. Division standards require them to be 95% confident they err by no more than 0.04 labor-hour from the true mean for each category. They divide the total space under all of their lines into square mile segments, so they can estimate the average hours needed per mile.  One clerk selected a convenient nonrandom sample of values for each of the three categories, just to get an idea of reasonable magnitudes before the more formal technical estimates. The three samples follow. The following questions concern the number of one-mile segments the crew should randomly select and gather data from in order to meet their accuracy standards.
 

Labor-hours per                 Labor-hours per                     Labor-hours per Thousand
Trimmed Tree                     Removed Tree                      Square Feet of Cut Brush
        0.86                                0.39                                                0.80
        0.74                                0.42                                                0.57
        0.72                                0.37                                                1.50
        0.78                                0.53
        0.21                                1.29
        0.94                                0.32
                                               0.36                                                                                    .
    0.71                               0.52                                               0.96

  S    0.25                                0.34                                               0.48
 

Schuler, Mark D., "A Successful Distribution Line-Clearance Program," Transmission & Distribution, April, 1993.

1.    Judging from the convenience samples'  information, which variable will require
       the largest sample?  Explain.

2.    Estimate the required sample size for each category.

3.    Suppose the line crew randomly selects the number of one-mile segments
       suggested in Question 2 and collects the appropriate set of n values to estimate
       each of the three labor requirements. The standard deviations computed from
       these three samples all fall short of the sample standard deviations computed
       from the convenience samples (0.25, 0.34, and 0.48). Does the line crew need to
       increase any of their sample sizes to maintain 95% confidence of an error of at
       most 0.04 labor-hour? Explain.
 
 

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