370 BELL SYSTEM TECHNICAL JOURNAL 



than six times the standard error, strongly indicating a significant differ- 

 ence between the forenoon and afternoon holding times. We conclude that 

 between 9 a.m. and noon the holding times are satisfactorily controlled 

 but that we should not attempt to include observations on afternoon hours 

 with them. Since the heaviest loads here occurred generally in the morning 

 we should confine our direct measurements or switch counts to these hours 

 for determining the engineering holding time. 



It may occasionally be well to investigate the possibility that certain 

 days of the week have, on the average, longer holding times than other days. 

 If the Newark 9-12 a.m. data are plotted by days of the week as in Fig. 3 

 we see that the averages for each day fluctuate considerably as shown by 

 the heavy dots. In testing these points the simple average of the a's for 



MON. TUE. WED. THU. FRI. SAT. 



DAY OF THE WEEK 



Fig. 3 — Variations in average holding times, 115 9-12 a.m. hours, by days of the week, 



Newark 



each day's hours is taken as an estimate of the standard deviation of the 

 homogeneous universe from which all the hours are presumed to be drawn. 

 Then with the weighted arithmetic means of the daily averages as the best 

 estimate available for the mean of the universe, each day's average is tested 

 to see whether it could reasonably have arisen from it. The ±2o- lines 

 which should include some 95% of the day-averages are shown on Fig. 3. 

 It is seen that two of the six points fall slightly outside these limits indicat- 

 ing a moderately significant difference in the holding time conditions for 

 Friday and Saturday. The sampling procedure to follow in such cases of 

 non-controlled populations is not rigorously definable. However, it is clear 

 that the samples should be drawn from the various groups of controlled 

 elements which probably go to make up the universe, and roughly in pro- 

 portion to the importance to be assigned to each such group. In our 

 example here we would probably want to draw samples of about equal size 

 from the calls of each week day in the week. 



