In an attempt to regain control of your time, you have been recording the time required, in minutes, to respond to each telephone call for the day. Before you make changes (such as referring certain types of calls to subordinates), you would like to have a better understanding of the situation. With calls grouped by type, the results for call lengths were as shown in Table 15.5.3. 

a. Draw box plots on the same scale for these four types of calls and describe the structure you see. 

b. Compute the average and standard deviation for each type of call. 

c. Which type of call appears to have the highest average length? Which has the lowest? 

d. Are the assumptions of normal distribution and equal variability for the one-way analysis of variance satisfied for this data set? Why or why not?

 e. Find the natural logarithm of each data value and draw box plots for these logarithms. 

f. Is the assumption of equal variability better satisfied using logarithms than using the original data?

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TABLE 15.5.3 Lengths of Telephone Calls Information Sales Service Other 0.6 5.1 5.2 6.3 1.1 1.7 2.9 1.2 1.0 4.4 2.6 3.1 1.9 26.6 1.2 2.5 3.8 7.4 7.0 3.0 1.6 1.4 14.2 2.6 0.4 7.0 8.4 0.8 0.6 3.9 0.6 2.2 3.1 26.7 12.3 1.2 7.7 4.2 1.9 4.8 2.8 17.3 7.2 1.4 7.8 2.7 4.3 3.4 3.4 13.3 1.3 2.0 TABLE 15.5.3 Lengths of Telephone Calls Information Sales Service Other 0.6 5.1 5.2 6.3 1.1 1.7 2.9 1.2 1.0 4.4 2.6 3.1 1.9 26.6 1.2 2.5 3.8 7.4 7.0 3.0 1.6 1.4 14.2 2.6 0.4 7.0 8.4 0.8 0.6 3.9 0.6 2.2 3.1 26.7 12.3 1.2 7.7 4.2 1.9 4.8 2.8 17.3 7.2 1.4 7.8 2.7 4.3 3.4 3.4 13.3 1.3 2.0